# 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.

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### Integral inequality on Bourgain Spaces

I'm studying the section about Bourgain spaces of Terence Tao's book "Nonlinear Dispersive Equations: Local and Global analysis". I'm trying to understar the proof of Lemma 2.11 and I'm ...
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### How do we show $\int_{[0,\:1)^2}\exp\left(-\frac{\left\|x-\frac{x_i+x_j}2\right\|^2}{\sigma^2}\right)\:{\rm d}x=\pi\sigma^2$ here?

Let $D=[0,\sqrt N)^d$ for some $N\in\mathbb N$, $x_i,x_j\in D$ and $\sigma>0$. In equation $(30)$ of this paper I've read that, if $d=2$, then \begin{equation}\begin{split}\int_D\exp\left(-\frac{\...
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### Contour Integral of $\sin(ax)/(b^2+x^2)$

I am trying to solve this integration. $$∫\frac{\sin(ax)}{b^2+x^2}\ dx$$ The limits of integration between $0$ to $c$ where $a, b,$ and $c > 0$ ... any idea. I tried the different similar methods ...
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### Why don't the bounds in this definite integral change?

The question This is probably a very basic question but I'm having a brain lapse and don't know why they didn't change the definite integral bounds from ($0 \rightarrow4$) to ($4 \rightarrow20$). I ...
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### Limits of Riemann sums left and mid endpoint rule.

In my calculus class we have begun talking about integrals. In particular we have begun talking about Reimann sums and how through the limit of a Reimann sum we can integral. But so far all our ...
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