Questions tagged [integration]
For questions about the properties of integrals. Use in conjunction with (indefinite-integral), (definite-integral), (improper-integrals) or another tag(s) that describe the type of integral being considered. This tag often goes along with the (calculus) tag.
4
questions with bounties
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Evaluate $\int_{0}^{1} \frac{K(k)E(k)^2-\frac{\pi^3}{8} }{k} \text{d}k$ and $\int_{0}^{1} \frac{E(k)^3-\frac{\pi^3}{8} }{k} \text{d}k$
Let $K(k),E(k)$ be the complete elliptic integral of the first kind and second kind respectively, where $k$ is the elliptic modulus. Consider four integrals,
$$\begin{aligned}
&I_1=\int_{0}^{1} \...
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answers
41
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+50
Filling functions on hypercubes given the function's integrals over each coordinate
$\newcommand\dif{\mathop{}\!\mathrm{d}}$
Suppose $f:[0,1]^2\rightarrow\mathbb{R}_{>0}$ and that:
$$\int_0^1{f(x,y)\dif x}=a(y),\hspace{1cm}\int_0^1{f(x,y)\dif y}=b(x),$$
for some known functions $a,...
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+250
When is $\int_0^\infty\int_0^\infty\int_0^R f(k,q,t,r)\,\mathrm{d}t\,dq\,\mathrm{d}k\stackrel{?}{=}g(r)$ where both $f$ and $g$ are known functions
I would like to know under which circumstances the following triple integral can be evaluated analytically as
$$
\int_0^\infty \int_0^\infty \int_0^R f(k,q,t,r) \,\mathrm{d}t \,\mathrm{d}q \,\mathrm{d}...
- 33
4
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1
answer
174
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+150
Evaluate the Integral $\int_{0}^{\infty}\ln\left(1+\pi\frac{2\cosh\left(t\right)+\pi}{t^{2}+\cosh\left(t\right)^{2}}\right)dt$
That's the essence of the problem: can the (in my opinion rather challenging) integral be solved or simplified:
$\int_{0}^{\infty}\ln\left(1+\pi\frac{2\cosh\left(t\right)+\pi}{t^{2}+\cosh\left(t\right)...
- 53