# Questions tagged [integration]

Concerns all aspects of integration, including the integral definition and computational methods. For questions solely about the properties of integrals, use in conjunction with (indefinite-integral), (definite-integral), (improper-integrals) or another tag(s) that typically describe(s) the types of the integrals being considered. This tag often goes along with the (calculus) tag.

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### Is this really a categorical approach to integration?

Here's an article by Reinhard Börger I found recently whose title and content, prima facie, seem quite exciting to me, given my misadventures lately (like this and this); it's called, "A ...
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### How weird can the boundary be so that the fundamental theorems of vector calculus hold?

Let $\Omega$ be a connected open set in $\Bbb R^n$. Suppose that I want theorems in multivariables calculus like divergence theorem or its relative like Green's identities or even Stoke's theorem to ...
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### Methodologies to Evaluate $\lim_{L\to \infty}\int_0^\infty \frac{\sin(Lx)}{x}\cos(x^3/3)\,dx$

In This Answer, I wrote "It is straightforward to show that $\displaystyle \lim_{L\to \infty}\int_0^\infty \frac{\sin(Lx)}{x}\,\cos(x^3/3)\,dx=\frac\pi2$." For completeness, I've included the "...
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### Double integral - transformation

I'm trying to calculate $$\iint_{\Omega } e^{(x+y^2)^{3/2}} \,\mathrm{d}A,$$ where $$\Omega =\{x,y>0 : x+y\leq 2\}.$$ Not sure where to go with it. I need to find a transformation and then ...
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### An extremely mysterious integral: $\int_0^1 \frac{k \tan^{-1}(t)}{k^2 + t^2}\mathrm d t$

$$f(n) = \int_0^1 \frac{n \tan^{-1}(t)}{n^2 + t^2}\mathrm d t \tag{n > 2}$$ Introduction: This is one of the most beautiful and mysterious integrals I've every encountered. It's very simple, but ...
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### Juantheron-like integral

While seeing this post, the following integral is just struck me $$\int_0^\infty \frac{dx}{(1+x^2)(1+\tan x)}\tag1$$ I have tried like what user @OlivierOloa did in his ...
### Integral of rational function over $\mathbb{H}^4$
Suppose I have a rational function of $8$ coordinates $a,b,c,d,e,f,g,h$ that I want to integrate over $\mathbb{H}^4$: ...