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# Questions tagged [integration]

Questions related to various forms of integration including the Riemann integral, Lebesgue integral, Riemann–Stieltjes integral, double integrals, line integrals, contour integrals, surface integrals, integrals of differential forms, ...

708 questions
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### Evaluate a pair of integrals involving dilogarithms over the unit interval

These are two variations on the "Bonus round" problem, expertly address by student at the end of his answer to A pair of integrals involving square roots and inverse trigonometric functions over the ...
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### Reference for calculating definite integral involving sines

Recently I accidentally discovered a simple, elementary derivation of the following identity, valid for any $n,k \in \mathbb N$: \begin{align*} \frac1\pi \int_0^\pi {\rm d}x \left(\!\frac{\sin nx}{\...
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### Can you add an extra e^x when integrating? [migrated]

So I've been given this problem to solve (pretend it's a fraction or click the link to see the question please) ∫ -26e^x-144 e^(2x) + 13e^x + 36 problem ...
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### Integration for Dirac-delta function

Is there any way to solve the integration below? or make it simple to eliminate the Dirac-delta function? $$\int_{-\infty}^\infty m(x)\delta(G(x)-g_c)f_X(x)dx$$ where $f_X(x)$ is a probability ...
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### Integrals of power towers

Let's assume $x\in[0,1]$, and restrict all functions of $x$ that we consider to this domain. Consider a sequence $\mathcal S_n$ of sets of functions, where $n^{\text{th}}$ element is the set of all ...
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### “Find a representation [using Mellin transform] of 𝑓(𝜇,𝛽) as Gauss hypergeometric function in variable 𝜇”

This is a follow-up to the first comment (by Nemo) to the posting Compute the two-fold partial integral, where the three-fold full integral is known . (I also just asked this as a comment to that ...

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