Matlab Infinity Integral

The following problems involve the integration of exponential functions. It uses the 'iterated' method when any of the integration limits are infinite. Learn more about matlab, integration, numerical integration MATLAB. In this tutorial numerical methods are used for finding the Fourier transform of continuous time signals with MATLAB are presented. In contour integration, contours provide a precise definition of the curves on which an integral may be suitably defined. Because these numbers are not symbolic objects, cosint returns floating-point results. We can use loops in a function so that MATLAB. Explanation: If we type sin(Inf) in MATLAB, we will get NaN as an input because MATLAB cannot find the value of sin(Inf). Exponential Integral for Floating-Point and Symbolic Numbers. Hi folks, today I'd like to introduce ChangQing Wang. Lower limit of x, specified as a real (finite or infinite) scalar value or a complex (finite) scalar value. quad for the integration, and numpy. terms tend to infinity. If you have a function that is only defined at discrete places, then you either need to use some other kind of calculation entirely or else replace the integral by a discrete approximation such as trapezoid calculation. These functions all solve 1-dimensional integration problems. In these cases, the interval of integration is said to be over an infinite interval. Numerical evaluation of the integral is called quadrature. The quadv function vectorizes quad for an array-valued fun. Still, many improper integrals can be evaluated exactly and others approximated numerically using commands we've already introduced. After the Integral Symbol we put the function we want to find the integral of (called the Integrand), and then finish with dx to mean the slices go in the x direction (and approach zero in width). Learn more about definite. Minimization of a integration function. Learn more about numerical integration, symbolic integration, infinite summation. I doubt you can maintain any numerical precision with such a construction. I need to have this function from negative infinity to infinity. A curve in the complex plane is defined as a continuous function from a closed interval of the real line to the complex plane: z : [a, b] → C. However, the result was way to small (order of magnitude 1e-39, whereas it should have been around 4e-14). I don't have all your input values to confirm it, but I think your integrand function is returning NaNs for some of the resulting input values. dirac(x, n) represents the n-th derivative of the delta distribution. We can now pull f(0) out of the integral (because it is a constant). Symbolic Math in Matlab Matlab has a reasonably powerful symbolic math ability. MATLAB live scripts support most MuPAD functionality, though there are some differences. This is the default method. However, in every case we've seen to this point the region \(D\) could be easily described in terms of simple functions in Cartesian coordinates. We can use loops in a function so that MATLAB. MATLAB Tutorial - NUMERICAL INTEGRATION ES 111 2/11 Take a look at the example of f(x) = 2x. The following problems involve the integration of exponential functions. I need to calculate the value of integral $\int_0^{\infty}(x^3-3x^2)\,e^{-4x}\,dx$. how to build an h-infinity controller with Learn more about h-infinity, controller. Otherwise, to troubleshoot the issue, break down your definition of fD into variables. For more about how to use the Integral Calculator, go to "Help" or take a look at the examples. That is, if we have a function x(t) with Fourier Transform X(f), then what is the Fourier Transform of the function y(t) given by the integral:. Matlab has a powerful symbolic math ability. Following on Mike's post, I just wanted to confirm that the following modification to Mike's code to handle the case where the upper limit of the inner integral (the integration variable being y) is a function of x:. The Riemann Integral I know of some universities in England where the Lebesgue integral is taught in the first year of a mathematics degree instead of the Riemann integral, but I know of no universities in England where students learn the Lebesgue integral in the first year of a mathematics degree. The PSE has a built-in function that Fie uses to test whether b is in–nite. Because at any point on e^x, the slope is equal to e^x. Check it out! read more >>. Similar definitions apply for and. So why not implement a numerical integration that takes on the value zero, if the function is numerically zero and infinity if it takes on nonzero equally signed values (for example, I'm not an expert). QUAD will call your function with a vector of inputs, not just a scalar. You solve this type of improper integral by turning it into a limit problem where c approaches infinity or negative infinity. The function output is infinite when the input is exactly 0. This solution is probably slightly faster, and works even with Ada83. There is a good discussion about it on Mathworks blog. The integrals defining C(x) and S(x) cannot be evaluated in the closed form in terms of elementary functions, except in special cases. Symbolic Math in Matlab Matlab allows you to create symbolic math expressions. This MATLAB function approximates the integral of the function z = fun(x,y) over the planar region xmin ≤ x ≤ xmax and ymin(x) ≤ y ≤ ymax(x). Both limits wanted to be from -Inf:Inf Your help is so important. We can use loops in a function so that MATLAB. The integral is improper if a or b is infinite or if f is undefined at a or b. I think they only part of the coding that I am having trouble with at the moment is calculating an improper integral with an upper bound of infinity. NaN Undefined numerical result (not a number). Matlab allows symbolic operations in several areas including: Calculus Linear Algebra. 75, from -infinity to "n" Lower limit is infinity - how do I solve upper limit "n"? Again it may be really easy and I may be spacing out on my basic calculus and Matlab skills. We will not be computing many indefinite integrals in this section. Then, I try to solve the limit. In cases like this, we can proceed by evaluating the integral numerically. Compute exponential integrals for numeric inputs. Double integration. Using MATLAB to Plot the Fourier Transform of a Time Function. MuPAD® notebooks will be removed in a future release. I am trying to calculate an integral in a loop however it is just returning infinity for every value; The integral in question is finite - I have tested it in wolfram alpha. Integration using matlab? how do i find integration of exp(-(y^2)/2) dy from minus infinity to x using matlab or any other software. But at the same time, the integral of e^x is also e^x. Show transcribed image text. Definite Integral. Por ejemplo, especifique 'WayPoints' seguido de un vector de números reales o complejos para indicar los puntos específicos que debe utilizar el integrador. Body of the package implementing numerical integration: package body Integrate is. I am trying to calculate an integral in a loop however it is just returning infinity for every value; The integral in question is finite - I have tested it in wolfram alpha. Let’s take a look at an example that will also show us how we are going to deal with these integrals. 3 Autominuten entfernt) unter dem Stichwort „MATLAB EXPO“ eingerichtet. what should I do?? my second question is that it is an array how could I have a continuous function because for example I need to access phi(. Trouble with MATLAB Triple Integral. You solve this type of improper integral by turning it into a limit problem where c approaches infinity or negative infinity. For definite integrals, int restricts the integration variable var to the specified integration interval. But at the same time, the integral of e^x is also e^x. That is, if we have a function x(t) with Fourier Transform X(f), then what is the Fourier Transform of the function y(t) given by the integral:. Compute exponential integrals for numeric inputs. Such integrals occur in fluid dynamics, elasticity, electrodynamics and biophysics to name but a few applications. Cosine Integral Function for Numeric and Symbolic Arguments. Let us now evaluate the integral of a function multiplied by an impulse at the origin. However, in every case we've seen to this point the region \(D\) could be easily described in terms of simple functions in Cartesian coordinates. But you have g. This is the default method. Warning: Infinite or Not-a-Number value encountered. I managed to calculate the integral by the means of both Mathcad and Mathematica. In contour integration, contours provide a precise definition of the curves on which an integral may be suitably defined. That assumes an elementary antiderivative exists. A comprehensive list of Fourier Transform properties. Learn more about definite. This function grows up to infinity in 0 (or 1) when alpha (or beta) < 1, and matlab has headache with the integral. Write a program to compute the Fresnel sine integral FresnelSi(x), which is defined as the integral of sin (π/2 t 2) from 0 to x. There is a good discussion about it on Mathworks blog. We will assume knowledge of the following well-known differentiation formulas : ,. So, if you could help me what is the way to get the integral then, it would be quite helpful. But at the same time, the integral of e^x is also e^x. Can anyone help with infinite integral computation in matlab? compute any infinite limit integral using computer and how to cut short its limit or change it to finite range integral so that we. I have a function that I put it's code below. Such integrals occur in fluid dynamics, elasticity, electrodynamics and biophysics to name but a few applications. 1BestCsharp blog 7,592,147 views. In order for the double integral to converge, you need g(x,y) --> -inf as max(x,y)-->inf, but this means that the output of the first integral call must approach -inf. The shifting property of impulses tells us that a signal can be decomposed into an infinite sum (integral) of scaled and shifted impulses. b) computes the definite integral. Let's say that we have a system with a disturbance that enters in the manner shown below. The quadv function vectorizes quad for an array-valued fun. In this section we introduce the Dirac Delta function and derive the Laplace transform of the Dirac Delta function. Algorithm 935: IIPBF , a MATLAB toolbox for infinite integral of products of two Bessel functions Article (PDF Available) in ACM Transactions on Mathematical Software 40(2) · February 2014 with. is well-defined only if f and g decay sufficiently rapidly at infinity in order for the integral to exist. One of the ways in which definite integrals can be improper is when one or both of the limits of integration are infinite. This integral should return 1. In cases like this, we can proceed by evaluating the integral numerically. To integrate a mathematical expression f means to find an expression F such that the first derivative of F is f. When the interval is in-nite, the kernel must be smooth across the diagonal, so the input value of behavior is ignored. For indefinite integrals, int implicitly assumes that the integration variable var is real. Such an integral is written as ∫b a f (x)dx where the term dx, referred to as the differential of x, indicates the variable of integration. Calling expint for numbers that are not symbolic objects invokes the MATLAB ® expint function. When this m-script is run it clears all variables and closes all open Figure Windows. I assumed it was integrable. In these cases, the interval of integration is said to be over an infinite interval. The arguments in the integral can also be switched to give two equivalent forms of the convolution integral. SnugglyHappyMathTime 8,111 views. Solve an Indefinite Integral - powered by WebMath. integral은 손으로 불가능한 적분 계산을 수치적으로 해줄 뿐 아니라, 위에서 본 이상 적분도 계산해 줍니다. Such integrals occur in fluid dynamics, elasticity, electrodynamics and biophysics to name but a few applications. (Type inf for the infinity symbol. MATLAB can find both an indefinite integral (i. We obviously can't add up an infinite number of terms, but we can add up the first n terms, like this:. If Y is a multidimensional array, trapz(Y) works across the first nonsingleton dimension. Compute the cosine integral function for these numbers. Calling expint for numbers that are not symbolic objects invokes the MATLAB ® expint function. MATLAB provides various ways for solving problems of differential and integral calculus, solving differential equations of any degree and calculation of limits. Infinite Interval. We work a couple of examples of solving differential equations involving Dirac Delta functions and unlike problems with Heaviside functions our only real option for this kind of differential equation is to use Laplace transforms. I have just started using matlab and was given the task to plot the graph. d eae dx = Integrating the exponential function, of course, has the opposite effect: it divides by the constant in the exponent: 1 edx e ax ax , a. Trapezoidal Integration. If the argument x represents a non-zero number, then 0 is returned. Perhaps the problem can be reformulated via some transformations so that the integrals remain bounded. Write a program to compute the Fresnel sine integral FresnelSi(x), which is defined as the integral of sin (π/2 t 2) from 0 to x. I have just started using matlab and was given the task to plot the graph. Some Useful Integrals of Exponential Functions Michael Fowler. Compute exponential integrals for numeric inputs. The upper limit for the integral. You may also do symbolic computations in the MATLAB command line, but be careful about the syntax difference between MATLAB scripts and MUPAD. Depending on its arguments, cosint returns floating-point or exact symbolic results. what should I do?? my second question is that it is an array how could I have a continuous function because for example I need to access phi(. MuPAD® notebooks will be removed in a future release. We can use loops in a function so that MATLAB. Lower saturation limit The lower limit for the integral. Wir haben ein weiteres Abrufkontingent im Victor's Residenz-Hotel München (ca. I want to integrate this function for the variables v and u (s is a variable with random value). I was facing problems so I put it here to get some solution. We use definite integrals to find areas such as the area between a curve and the x-axis and the area between two curves. The default is inf. In these cases, the interval of integration is said to be over an infinite interval. The Dirac delta is not strictly a function, because any real function that is equal to zero everywhere but at a single point must have a total integral equal to zero, but for many purposes this definition can be manipulated as a function. If one or both integration bounds a and b are not numeric, int assumes that a <= b unless you explicitly specify otherwise. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts. Expert Answer 100% (1 rating) Previous question Next question Transcribed Image Text from this Question. At line 64, I noticed that I wrote a / instead of * (kJ to J is obviously *1000 not /1000 ;) ) So after I corrected that mistake, the Warning: "Infinite or Not-a-Number value encountered" occurred (at the matlab-function integral, line 106 to 108). Because these numbers are not symbolic objects, cosint returns floating-point results. I have just started using matlab and was given the task to plot the graph. But apart from discouragement I haven't got anything. I don't have all your input values to confirm it, but I think your integrand function is returning NaNs for some of the resulting input values. I've used scipy. Matlab has a powerful symbolic math ability. vpaintegral uses variable-precision arithmetic in contrast to the MATLAB integral function, which uses double-precision arithmetic. When integrating over infinite intervals do so explicitly, rather than just using a large number as the endpoint. At line 64, I noticed that I wrote a / instead of * (kJ to J is obviously *1000 not /1000 ;) ) So after I corrected that mistake, the Warning: "Infinite or Not-a-Number value encountered" occurred (at the matlab-function integral, line 106 to 108). Inf Infinity. In contour integration, contours provide a precise definition of the curves on which an integral may be suitably defined. If Y is a vector, trapz(Y) is the integral of Y. In computerized or numerical methods, a numerical integration can be performed by a number of algorithms that calculate the approximate value of definite integrals. Trouble with MATLAB Triple Integral. I doubt you can maintain any numerical precision with such a construction. For indefinite integrals, int implicitly assumes that the integration variable var is real. If you want to compute the power or energy of discrete time signals, then you need to use the corresponding definitions:. Integrate besseli(5,25*u). » Integrate can evaluate integrals of rational functions. Das Zimmerkontingent im Infinity Hotel ist leider bereits ausgebucht. MATLAB provides an int command for calculating integral of an expression. But now, I must to transform this values in a Matlab function, i. In general, if the function is separable but the integral can't be solved analytically it will be much more efficient to compute the product of two one-dimensional integrals than to directly compute the two-dimensional integral. DOWNLOAD DIRECTORY FOR MATLAB SCRIPTS Download and inspect the mscripts and make sure you can follow the structure of the programs. % The builtin 'quad' function is not very robust and is also quite slow. Cosine Integral Function for Numeric and Symbolic Arguments. Then, I try to solve the limit. I know there are lots of photos but I figured it is best to learn more MATLAB for my future endeavors in my field (I am a newbie at MATLAB). Matlab allows symbolic operations in several areas including: Calculus Linear Algebra. When this m-script is run it clears all variables and closes all open Figure Windows. m') that is much much better. Symbolic Math in Matlab Matlab allows you to create symbolic math expressions. At line 64, I noticed that I wrote a / instead of * (kJ to J is obviously *1000 not /1000 ;) ) So after I corrected that mistake, the Warning: "Infinite or Not-a-Number value encountered" occurred (at the matlab-function integral, line 106 to 108). Otherwise, to troubleshoot the issue, break down your definition of fD into variables. dirac(x, n) represents the n-th derivative of the delta distribution. Because these numbers are not symbolic objects, you get floating-point results. Calling expint for numbers that are not symbolic objects invokes the MATLAB ® expint function. » Integrate can evaluate integrals of rational functions. We can simplify this integral by noting that because the impulse is zero everywhere except when t=0 we can replace δ(t)·f(t) by δ(t)·f(0). Modernization of Numerical Integration, From Quad to Integral Posted by Cleve Moler , May 23, 2016 The MATLAB functions for the numerical evaluation of integrals has evolved from quad , through quadl and quadgk , to today's integral. I have a vague idea how to do it with using a trap and a series of loops, but most of the documentation uses a function, and I only have a series of data (that and my data is finite, but I'm looking for the infinite integral). to evaluate infinite integral. To derive an expression for the indefinite integral of a function, we write − int(f); For example, from our previous example − syms x int(2*x) MATLAB executes the above statement and returns the following result − ans = x^2 Example 1. The Dirac delta is not strictly a function, because any real function that is equal to zero everywhere but at a single point must have a total integral equal to zero, but for many purposes this definition can be manipulated as a function. m') that is much much better. cond computes the condition number according to Equation , and can use the one norm, the two norm, the infinity norm or the Frobenius. Only that I am in the same time trying to learn Matlab. 1) but because of having array, index should be just positive. Choose a web site to get translated content where available and see local events and offers. We will not be computing many indefinite integrals in this section. Evaluating a multiple integral involves expressing it as an iterated integral, which can then be evaluated either symbolically or numerically. The integral calculator allows you to enter your problem and complete the integration to see the result. Documents Flashcards Grammar checker. Vectorization is very important to e¢ ciency in Matlab, so we require that. So why not implement a numerical integration that takes on the value zero, if the function is numerically zero and infinity if it takes on nonzero equally signed values (for example, I'm not an expert). This function grows up to infinity in 0 (or 1) when alpha (or beta) < 1, and matlab has headache with the integral. Numerical Integration with Infinity as the upper Learn more about integration, matlab. *exp(-u*25) by using both integral and vpaintegral. We can simplify this integral by noting that because the impulse is zero everywhere except when t=0 we can replace δ(t)·f(t) by δ(t)·f(0). It also supports contour integration along piecewise linear paths. My question still remains unsolved. We have developed and tested a MATLAB toolbox called IIPBF. 1 FOURIER SERIES FOR PERIODIC FUNCTIONS This section explains three Fourier series: sines, cosines, and exponentials eikx. Asked by the more the integral decreases. Integrate besseli(5,25*u). In contour integration, contours provide a precise definition of the curves on which an integral may be suitably defined. The Rayleigh Integral Method in Matlab | The Rayleigh integral is an equation relates the sound pressure (or velocity potential) at a point in a half-space to the vibration of a plate that in an. Symbolic Differentiation and Integration (4:36) MATLAB has a symbolic math toolbox that also supports differentiation and integration. If you would like to perform pure symbolic computations, you may type MUPAD in MATLAB command line and do it from there. Similar definitions apply for and. enough to save the numeric integral: you are integrating to infinity and the. This increases the chance of a correct answer – any function whose integral over an infinite interval is finite must be near zero for most of that interval. Expert Answer 100% (1 rating) Previous question Next question Transcribed Image Text from this Question. I managed to calculate the integral by the means of both Mathcad and Mathematica. Fresnel Cosine Integral Function for Numeric and Symbolic Input Arguments. MATLAB Programming Tutorial #14 Numerical Integration Complete MATLAB Tutorials @ https://goo. This was a very helpful post as I was wondering how I would achieve a double integration where the limits could be Inf. Free definite integral calculator - solve definite integrals with all the steps. Now f(x) is just a constant equal to D. If your variable of integration is y, and m and T are to remain symbolic (no definite value given for them before the integration), then you will have trouble finding an analytic integral. integration of a piecewise function. The shifting property of impulses tells us that a signal can be decomposed into an infinite sum (integral) of scaled and shifted impulses. Let’s take a look at an example that will also show us how we are going to deal with these integrals. int(f, x = a. And as I've got some other functions similar to mentioned, which I need to solve numerically, I would need someone just to tell me how to write a proper function for that. i,j The imaginary unit -1. In order for the double integral to converge, you need g(x,y) --> -inf as max(x,y)-->inf, but this means that the output of the first integral call must approach -inf. Numerical Integration with Infinity as the upper Learn more about integration, matlab. Matlab allows symbolic operations in several areas including: Calculus Linear Algebra. Inf, which is the way that Matlab represents in–nity. I don't have all your input values to confirm it, but I think your integrand function is returning NaNs for some of the resulting input values. Body of the package implementing numerical integration: package body Integrate is. Doing Physics with Matlab Quantum Mechanics Bound States 2 add to the m-script to define your own potential well. q = integral(fun,xmin,xmax,Name,Value) especifica opciones adicionales con uno o más argumentos de par Name,Value. To evaluate the integral symbolically, we can proceed in two stages. where by erf(x) MATLAB is referring to the function erf(x) := 2 √ π Z x 0 e−y2dy, which is to say, MATLAB hasn’t actually told us anything. I have just started using matlab and was given the task to plot the graph. The PSE has a built-in function that Fie uses to test whether b is in-nite. I want to integrate this function for the variables v and u (s is a variable with random value). Integrate besseli(5,25*u). Compute exponential integrals for numeric inputs. Defining a symbolic function with an integral. This function accepts one argument only. Because these numbers are not symbolic objects, cosint returns floating-point results. Learn more about fourier, int, sym, symbolic, integration, continuous, time, transform, evaluate. We begin by discussing the evaluation of iterated integrals. For example, specify 'WayPoints' followed by a vector of real or complex numbers to indicate specific points for the integrator to use. Can anyone help with infinite integral computation in matlab? compute any infinite limit integral using computer and how to cut short its limit or change it to finite range integral so that we. Notice there is no 'integral' on the right side. Maclaurin series coefficients, a k can be calculated using the formula (that comes from the definition of a Taylor series) where f is the given function, and in this case is sin(x). eps Accuracy of floating-point precision. of Statistics %% % Symbolic Math Toolbox. f = @(x) 1. Of course it can't handle all possible integrands. Some Useful Integrals of Exponential Functions Michael Fowler. you see that I make an array, and I access to the elements 1 to 3000. In general, if the function is separable but the integral can't be solved analytically it will be much more efficient to compute the product of two one-dimensional integrals than to directly compute the two-dimensional integral. Counting it on $[0, 1]$ interval is simple using the trapezoidal or Simpson's rule. I managed to calculate the integral by the means of both Mathcad and Mathematica. Still, many improper integrals can be evaluated exactly and others approximated numerically using commands we've already introduced. *exp(-u*25) by using both integral and vpaintegral. As seen above, I try to first solve the integral of Pix, from minus infinite to infinite. Por ejemplo, especifique 'WayPoints' seguido de un vector de números reales o complejos para indicar los puntos específicos que debe utilizar el integrador. When the interval is in-nite, the kernel must be smooth across the diagonal, so the input value of behavior is ignored. To compute the two-argument exponential integral, use sym to convert the numbers to symbolic objects, and then call expint for those symbolic objects. Hi folks, today I'd like to introduce ChangQing Wang. Computing Fourier Series and Power Spectrum with MATLAB By Brian D. /sqrt(1-cos(x)) integral(f,0,2*pi) quadgk(f,0,2*pi). +, *, ' e tc. For example, nd out ∫ 1 0 1 (x+1) p x dx >## define the integrated function >integrand <- function(x) {1/((x+1)*sqrt(x))}. MATLAB Commands - 4 Special Variables and Constants ans Most recent answer. Conditions for the existence of the convolution may be tricky, since a blow-up in g at infinity can be easily offset by sufficiently rapid decay in f. If the argument x represents a non-zero number, then 0 is returned. In this tutorial numerical methods are used for finding the Fourier transform of continuous time signals with MATLAB are presented. If the integral has the limits [0, Inf] you can omit the abs. Let us use for instance sage to get the exact value of the integral (and some numerical approximation of this exact value). ) is defined. When this m-script is run it clears all variables and closes all open Figure Windows. Matlab Integral Infinity. When we calculate the integral from an interval. To compute the integral for spacing other than one, multiply Z by the spacing increment. I am experiencing some frustration over the way matlab handles numerical integration vs. (Type inf for the infinity symbol. For n-fold integration, scipy provides the function nquad. The integral is improper if a or b is infinite or if f is undefined at a or b. But you have g. Solving the integral by hand would include thousands or millions of calculations. For more about how to use the Integral Calculator, go to "Help" or take a look at the examples. Depending on its arguments, cosint returns floating-point or exact symbolic results. If you have a function that is only defined at discrete places, then you either need to use some other kind of calculation entirely or else replace the integral by a discrete approximation such as trapezoid calculation. If your variable of integration is y, and m and T are to remain symbolic (no definite value given for them before the integration), then you will have trouble finding an analytic integral. > I am not familiar which of the quadrature routines of matlab uses > gaussian rules, but you can google for "16 points gaussian > quadrature". Perhaps the problem can be reformulated via some transformations so that the integrals remain bounded. jar Library to the Apache Tomcat folder of global JARs:. Such an integral is written as ∫b a f (x)dx where the term dx, referred to as the differential of x, indicates the variable of integration. Doing Physics with Matlab Quantum Mechanics Bound States 2 add to the m-script to define your own potential well. Creative Exercises. There is a good discussion about it on Mathworks blog. I don't have all your input values to confirm it, but I think your integrand function is returning NaNs for some of the resulting input values. I am experiencing some frustration over the way matlab handles numerical integration vs. m Set of 1 to 4 parallel wires aligned in the Z direction Calculations based upon the Biot-Savart Law: magnetic field B, line integral C ³ B dL, curl uB, magnetic flux A ³ B dA and divergence B simpson1d. We begin by discussing the evaluation of iterated integrals. They both do the same think, but the name "integral" is easier to remember, easier to find and easier to use. For indefinite integrals, int implicitly assumes that the integration variable var is real. At line 64, I noticed that I wrote a / instead of * (kJ to J is obviously *1000 not /1000 ;) ) So after I corrected that mistake, the Warning: "Infinite or Not-a-Number value encountered" occurred (at the matlab-function integral, line 106 to 108). In cases like this, we can proceed by evaluating the integral numerically. Do you want to calculate integral of a function right now ? Ok, let see In Matlab, "integral", "integral2" and "integral3" refer to "adaptive integral", "double integral", "triple integral", respectively 1. Let us now evaluate the integral of a function multiplied by an impulse at the origin. q = integral(fun,xmin,xmax,Name,Value) specifies additional options with one or more Name,Value pair arguments. Integration Method Description 'auto' For most cases, integral2 uses the 'tiled' method. I think they only part of the coding that I am having trouble with at the moment is calculating an improper integral with an upper bound of infinity. Do this using the command syms >>syms x y z a; This command basically tells the software that you will be using the symbols x, y, z, and f in forthcoming symbolic expressions. The integrals defining C(x) and S(x) cannot be evaluated in the closed form in terms of elementary functions, except in special cases. The notation on the left side denotes the definite integral of f(x) from a to b. I’m teaching myself ODE using Khan Academy and learning about Laplace Transforms requires you to take integrals from 0 to infinity and I’m not sure how this affects the integral of the Dirac delta function. We work a couple of examples of solving differential equations involving Dirac Delta functions and unlike problems with Heaviside functions our only real option for this kind of differential equation is to use Laplace transforms. you see that I make an array, and I access to the elements 1 to 3000.