# Tagged Questions

48 views

### Mean value over an infinite interval

I just need a sanity check, been thinking about this all morning. If we use the Mean Value Theorem on a function over the infinite interval (suppose the function's domain is unbounded), i.e. ...
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### Showing a limit exists

No solution please. I want to show that the following limit exists $$\lim_{T\to \infty}\frac{1}{2T}\int_{-T}^{T}f(x)\,\overline{g(x)}\,dx$$ where $f$ and $g$ are finite linear combinations of ...
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### Find $\int_0^{+\infty}\cos 2x\prod_{n=1}^{\infty}\cos\frac{x}{n}dx$

Evaluate the following integral $$\int_0^{+\infty}\cos 2x\prod_{n=1}^{\infty}\cos\frac{x}{n}dx$$ I was thinking of a way which do not need to explicitly find the closed form of the infinite product, ...
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### Why $\int^{+\infty}_{-\infty} x \, dx \neq 0$

We are going over improper integrals and tests for convergence in my Calc II course. During a lecture, my professor warned us to take caution when taking integrals from negative infinity to infinity. ...
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### Integral with several parameters

Let $r>0$. Find $(p,q) \in \mathbb{R}^{2}$ such that the integral: $$\int_{1}^{\infty}{\frac{(x^{r}-1)^{p}}{x^{q}}} ~dx$$ converges and for those values calculate it. I've already ...
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### test convergence of improper integrals 4

Test the convergence of improper integrals : $$\int_1^2{\sqrt x\over \log x}dx$$ I basically have no idea how to approach a problem in which log appears. Need some hint on solving this type of ...