Questions tagged [integral-equations]

Questions which deal with or solve for functions expressed in integral form, i.e., one or more unknown functions that appear under an integral sign.

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31 views

How do you plot an integral on mathematica? [closed]

How do I plot this integral on mathematica? I am trying to do this by hand but want to check on mathematica to see if I am doing it correct.
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35 views

How would you plot the integral on [a,b] in terms of one variable x in mathematica?

How would you plot the definite integral ∫4 dx on interval [a,b] where a=0 and b=4 are the upper and lower bounds on mathemetmatica? The reason why I am asking is because I am practicing graphing ...
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1answer
97 views

How do I plot a definite integral on Mathematica?

I am not sure how to put this in good format, but I want to plot this on Mathematica: $$ u(t) = \frac{1}{4\pi t} \int\mathrm dy\ \mathrm e^{-y^2/(4t)}\ y\ (1 - y^2) $$ on the interval $ [a, b] $ ...
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1answer
96 views

How can I always get the simplest solution from Integrate? [closed]

When I evaluate this. Integrate[1/(x (1 + x^4)^(1/4)), x] // FullSimplify In 11.3 I get ...
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1answer
90 views

How to calculate integration with undefined functions?

There are two functions inside the integral symbol, one is related to the independent variable and the other is independent of the independent variable. Both are the derivative and Tload is a ...
2
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0answers
36 views

Computing integral using trapezoid method and simpsons' rule for a given partition

I am given f[x_]=E(x^-x)-1 on interval [1,4] and partition ...
1
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0answers
130 views

How to solve ode with convolution?

my question is as this and i want to get the solution of this ode x(t) $ ({M_{33}}{\rm{ + }}{{\rm{m}}_{33}})x''(t) + \int\limits_{ - \infty }^t {x'(tau){K_{33}}(t -...
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1answer
90 views

Double integration of an exponential function which includes a Csch function and complex numbers

Mathematica couldn't solve following using just integrate function. I checked on interpolating as well, that also turned to be a dead end. Can someone help me with evaluating this integral? If it ...
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0answers
52 views

How solve integral with three moment and delta function [closed]

I am trying solve this integral in mathematica: \begin{equation} \int \dfrac{d^3 p_3}{(2\pi)^3 2 E_3} \dfrac{d^3 p_4}{(2\pi)^3 2 E_4}(p_1 p_2)(p_3 p_4) \delta (p_3 + p_4 - p_1 - p_2). \end{equation} ...
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1answer
155 views

Solving partial integro-differential equation

I want to solve a partial integro-differential equation of this form: using NDSolve, something like ...
3
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1answer
162 views

Inverse Laplace transform of this complicated function

I have been solving a coupled PDE system analytically and I need to find the inverse Laplace transform of $(1)$ and get $T(x,y)$. $s$ is the Laplace domain variable and $\alpha, \beta, \gamma, T_{fi}, ...
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1answer
35 views

FindRoot: equation with integral on parametric domain

Writing: ...
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1answer
70 views

Solve an Integral-differential equation with DSolve

I do not understand why the following code does not solve the equation: ...
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1answer
71 views
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0answers
30 views

Help with NIntegrate with singularity and variable integration limit

I have a function of the type: $$ F(x,z)= \int_{-\infty}^{\infty} dx' \int^{z}_{-\infty} dz' f(z,z',x,x')\frac{\partial g(z',x')}{\partial z'}$$ where the integration order may be interchanged. I ...
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1answer
64 views

Definite Integral [closed]

I am not able to do the following integration. \begin{equation} \int_{0}^{a} x\sin^2 \left(\frac{n \pi x}{a} \right)dx \end{equation} It shows an error that "more input is needed". The mathematica ...
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2answers
85 views

Can't solve for y in a fairly simple work done by magnetic field equation

The equations below are essentially calculations for a railgun-type mechanism (here is a good image description). I also drew an image using my own variables as definitions: I assumed that ...
2
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2answers
106 views

Trouble second-order ordinary differential equations with integral terms

I am a beginner of mma. During the learning of differential equations, I encountered a very difficult problem, a second-order system of ordinary differential equations with integral terms. This ...
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2answers
86 views

Problem with FindRoot function

I have set up a code to solve simultaneous integral equations. These result essentially from taking integrals of the Fermi-Dirac distribution. Although there are no obvious problems with the code it ...
1
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1answer
97 views

Regression to fit data with an integral equation

I have a set data and I know that this data are best fitted by the following equation, assuming that f($\tau$) is a log normal distribution and $M_{eq}$ = 1.5: $M(t,\tau)= M_{eq} \int (1-e^{-t/\tau}) ...
1
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1answer
113 views

Solving IDE system using FDM based on NDSolve`FiniteDifferenceDerivative

I wanted to solve the following system of integro-differential equations (IDEs) using finite difference method (FDM). $y_1''(t)+t^2y_1(t)-y_2''(t)+\int\limits_0^t[(t-x)y_1(x)+y_2(x)]\mathrm{d}x=(2+t^...
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2answers
180 views

solve the iterative integral equatio [duplicate]

The following code is incorrect, please specify my mistakes ...
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1answer
64 views

Solve integral equation by iteration

For[{n = 1, y[0][x_] = 1}, n < 4, n++, y[n][x_] = 1 + Integrate[y[n - 1][t]^2 + t^2, {t, 0, x}]; Print[{n, y[n][t]}]] here how can I get table of values ...
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2answers
48 views

problem with constant variables

Variable x is supposed to be constant, but the program calculates for each variable x, 100 numbers of x. I want all my x variables to have the same definition, but the program constantly changes each ...
2
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2answers
107 views

Unexpected limit result (was: How to fix the limit problem?)

MATHEMATICA fails in proving that Limit[ Integrate[ x^(x - 1) , {x, t, 2*t} ] , t -> 0 , Direction -> "FromAbove" ] == Log[2] How to fix ...
4
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1answer
253 views

How to speed up the integral in NDSolve?

On the MMA.SE, there have been several question on how to solve equations including integral using NDSolve, see example 1, example 2, and example 3. Many people, ...
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0answers
95 views

How to integrate this expression one time? [duplicate]

How can I integrate this expression? I want to have the second derivative of V i.e. V''[r]. Note that, you can multiply it be ...
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1answer
123 views

How can I create loop for this iteration integration [closed]

I have definite integral of the form $$f(x)=\int_{-\pi}^\pi\frac{x^2-1}{(x^2-1)^2+x^2+y^2+f(x)}dxdy$$ I want to make a code to calculate $f(x)$ numerically, starting from $f(x)=0$ and stopping when ...
3
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4answers
474 views

How can I simplify $\lim_{n\to \infty } \, \int_0^n e^{-x} \left(1-\frac{x}{n}\right)^n \, dx$?

How can I simplify $\lim_{n\to \infty } \, \int_0^n e^{-x} \left(1-\frac{x}{n}\right)^n \, dx$ ? Limit[Integrate[(1 - x/n)^n/E^x, {x, 0, n}], n -> Infinity] ...
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1answer
47 views

Convolve doesn't yeild expected answer, nor does integrate

I am convolving, or trying to, a Gaussian and a Lorentzian as follows: ...
5
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1answer
189 views

Solving partial differential equation involving Hilbert transform

While solving one research paper published in Physical Review Letters, I came across the following equation and I am unable to solve it. $$\frac{\partial f}{\partial t}−(\mathcal{H}(f)\left(\frac{\...
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1answer
57 views

Area of a parametric plot with interpolating functions

I am looking for the area of a parametric plot defined by two solutions (defined as: VVLt & PVLt) of Numerically solved differential equations. The problem is when i'm trying to integrate the two, ...
4
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2answers
339 views

Nonlinear boundary value problem of ODE involving principal value of integral

I have asked a question on a nonlinear eigenvalue problem (EVP). And I have worked on these for a week but I cannot solve it. I think I should first try to solve the related ODE boundary value problem ...
0
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1answer
75 views

Delayed differential equation with convolution

So I have a differential equation : $\left\{\begin{split} & c'(t) = \alpha q(t) c(t)^{2/3} - \beta(1 - q(t))c(t)\\ &\chi'(t) = \kappa c(t) q(t) \\ & q(t) = \int_{-\infty}^t \Big( ...
4
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3answers
210 views

Numerical solution of a singular integral equation

I am looking to approximate the solution u of the following equation using discretization method or any other idea. Is there any way on how to find a numerical ...
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1answer
40 views

Inverse stochastic problem solution

I am trying to determine a probability density $p(\mu)$ such that, when $\mu$ is inputted into a forward simulation equation: $d \sim \mathcal{N}(\mu,0.1)$, I obtain a distribution on $d\sim \mathcal{...
1
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1answer
67 views

How can I solve this integration or does it have a closed form solution?

The integral I am dealing with is below. I need to find the closed-form expression of this integral. $\int_0^\infty \ln(1+\frac{A}{1+B+Cx})\frac{e^{-x/M}}{M}dx$ Here, $A$, $B$, $C$ and $M$ are ...
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0answers
42 views

Calculate a definite integral containing an ExpIntegral

I need to calculate the following integral Integrate[Exp[-(y/bn)] (-y)^c ExpIntegralE[d, p y], {y, 0, z/x}] Where $z<0,z\in \mathbb{R}$, $x\in\mathbb{R},x>...
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1answer
120 views

Substitution into integral [duplicate]

I have to do a substitution (u = pi/2-x) into an definite integral, which I have defined as f[u]. When I evaluate my code, no ...
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0answers
30 views

Using `Integrate` and or `FourierTransform`

I have some general questions about Integrate and FourierTransform. Firstly with ...
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0answers
68 views

Solving a finite Hilbert transform from 2D thin wing theory

I have a problem where I know $w(x) =1$ and want to find $u(x)$. It's a well-known problem I am recreating, from a 1972 paper. Note the paper doesn't solve the problem, the integral equation, it just ...
2
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0answers
104 views

Can this integral equation problem $\int_\Gamma \frac{e^{ik|x-y|}}{4\pi|x-y|}\varphi(y) \, \mathrm{d} y = u_{x_0}^{in}(x)$ be solved?

I am not sure if Mathematica is capable of solving integral equations in 2D/3D. I found this page in the documentation, but this is just for 1D. The following is what I would like to solve, it can ...
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2answers
298 views

Solving Fredholm Equation of the second kind

Consider the Fredholm Equation of the second kind, $$\phi(x) = 3 + \lambda \int_{0}^{\pi} \text{cos}(x-s) \, \phi(s) \,ds$$ Where the analytical solution is found as, $$\phi(x) = 3 + \frac{6\lambda}...
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3answers
643 views

Solving an integro-differential equation with Mathematica

I try to solve a nonlinear integro-differential equation with this code. Here i used a periodic condition. ...
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1answer
95 views

Solving an integral equation analytically [closed]

I have an inegral equation like this $\qquad n(\phi)=\int_0^\sqrt{\phi} f(w)\sqrt{2w+\phi}dw$. I need to find $f(w)$ analytically. Here $n(\phi)$ is known. Here $n(\phi) = -\frac{2}{\delta ^2 \phi ...
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1answer
76 views

It's wrong the solution to definite integral from Mathematica 11.3? [closed]

I'm solving the exercise 23 from 4.8 section from "The Calculus 7th Leithold" (I use the Spanish edition "El Cálculo 7"), I write the solution in (physical) notebook, was 8*sqrt(2)/3, but when run in ...
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0answers
60 views

Integral of intersection of a spiral and a circle

I need to prove that for a full turn of a logarithmic spiral (independent from the constant tangent of it) and a straight line on the z axis, the logarithmic spiral always covers more space-time in ...
3
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1answer
185 views

Using DSolve to solve an integral equation

I've the following integral (or DE) that I need to solve (for $x(t)$ and all the constants are known, real and positive): $$k\cdot\theta\left(t-m\right)+(n-k)\cdot\theta\left(t-v\right)=$$ $$x(t)\...
3
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2answers
222 views

Solution or artifact?

I am trying to increase the precision of the code ...