# 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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### 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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### 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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### 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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### 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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### 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 ...
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### 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 ...
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Writing: ...
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### Solve an Integral-differential equation with DSolve

I do not understand why the following code does not solve the equation: ...
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Given: ...
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### 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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### 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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### 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 ...
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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### 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 ...
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### solve the iterative integral equatio [duplicate]

The following code is incorrect, please specify my mistakes ...
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### Solve integral equation by iteration

For[{n = 1, y[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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### 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 ...
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### Where is a small difference between result of normal finite integral and taking limit on definite integration from?

Here's my code. ...
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### 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 How to fix ...
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### 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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### 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 ...
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 ...
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### 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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### Convolve doesn't yeild expected answer, nor does integrate

I am convolving, or trying to, a Gaussian and a Lorentzian as follows: ...
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### 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. ...