# 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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### Sum of integrals is not the same as the integral of the sum

I came across this behaviour in integration (note I put b=2 in the end to make sure that MA is not trying to use complex b): <...
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### Numerically solving an ODE whose right-hand side involves an integral

In a 1955 paper on surfaces of constant negative Gaussian curvature, Marc-Henri Amsler defines a function $w(x)$ by giving the ordinary differential equation $$w'(x)=\frac{1}{x}\int_0^x \sin(w(t))dt,$$...
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### Solving integro-differential equation [closed]

I would like to solve the integro-differential equation of the form $$\left( -n \int_0^b b db + \frac{i \Lambda l_P^2}{9V_c}\frac{d}{db}+b^2+k\right)\psi(b)=0.$$ I followed the steps in Solve an ...
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### How to find the expectation $\mathbb{E}\left[ a \mathcal{Q} \left( \sqrt{b } \gamma \right) \right]$?

I'm trying to find the following expectation $$\mathbb{E}\left[ a \mathcal{Q} \left( \sqrt{b } \gamma \right) \right],$$ where $a$ and $b$ are constant values, $\mathcal{Q}$ is the Gaussian Q-function,...
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### Getting two different results for the same computation

I have the following two codes: ...
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### Integral of $r \frac{2^{r-1} \log (2) e^{-\frac{\sqrt{2^r-1}}{b}} \left(2^r-1\right)^{\frac{d}{2}-1}}{b^d \Gamma (d)}$ with Mathematica

I'm trying to find the integral given below with Mathematica $\int_0^{\infty } r \frac{2^{r-1} \log (2) e^{-\frac{\sqrt{2^r-1}}{b}} \left(2^r-1\right)^{\frac{d}{2}-1}}{b^d \Gamma (d)} \, dr$ However, ...
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### Gaussian Integral incorrect

I'm trying to learn about the Gaussian Normal distribution using Mathematica. So I defined my Gaussian like this ...
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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 ...
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### Why this change gives different results in Integrate?

I'm new in Mathematica and can't understand why changing a number from Real to Integer is giving different results in my equations: ...
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### Testing Turbulence Models

In the 90s, several turbulence models were proposed. Using Mathematica vv 10-12.1 we tested two models: 1) Spalart-Allmaras turbulence model (SA) for aerodynamic applications, published in AIAA ...
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### How should one evaluate this integral [closed]

How does one go about evaluating such an integral where E and V are constants? $\int\sqrt{E-Vx^8}dx$
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### How to 3DPlot a triple integral in cartesian coordinates

I am trying to make a 3d graph of the triple integral in cartesian coordinates. I am positive that I have been filling out the correct parameters but I am unsure what could be wrong. Additionally I ...
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### How to solve a system of integral equations?

I have a system of two integral equations ...
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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 ...
140 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 ...