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43 votes

Prove: $\int_0^\infty \sin (x^2) \, dx$ converges.

calculus integration improper-integrals asked Feb 2, 2012 at 21:43
math.stackexchange.com

36 votes

Prove: $\binom{n}{k}^{-1}=(n+1)\int_{0}^{1}x^{k}(1-x)^{n-k}dx$ for $0 \leq k \leq n$

probability special-functions binomial-coefficients definite-integrals asked Nov 28, 2011 at 22:00
math.stackexchange.com

30 votes

Prove that $f$ continuous and $\int_a^\infty |f(x)|\;dx$ finite imply $\lim\limits_{ x \to \infty } f(x)=0$

calculus integration asked Feb 11, 2012 at 17:53
math.stackexchange.com

29 votes

Prove: $\int_0^1 \frac{\ln x }{x-1} d x=\sum_1^\infty \frac{1}{n^2}$

calculus integration improper-integrals asked Feb 11, 2012 at 20:09
math.stackexchange.com

29 votes

An integrable and periodic function $f(x)$ satisfies $\int_{0}^{T}f(x)dx=\int_{a}^{a+T}f(x)dx$.

calculus definite-integrals periodic-functions asked Dec 26, 2011 at 15:32
math.stackexchange.com

26 votes

Finding the minimum cut of an undirected graph

algorithms graph-theory asked Sep 2, 2012 at 8:47
cs.stackexchange.com

19 votes

Is the set of Turing machines which stops in at most 50 steps on all inputs, decidable?

computability undecidability asked Aug 9, 2012 at 10:27
cs.stackexchange.com

19 votes

Does $\int_{1}^{\infty}\sin(x\log x)dx $ converge?

calculus improper-integrals asked Feb 7, 2012 at 16:18
math.stackexchange.com

17 votes

$K\subseteq \mathbb{R}^n$ is a compact space iff every continuous function in $K$ is bounded.

real-analysis general-topology compactness asked Jan 16, 2012 at 19:28
math.stackexchange.com

15 votes

Is it decidable whether a TM reaches some position on the tape?

computability turing-machines undecidability asked Aug 10, 2012 at 19:10
cs.stackexchange.com

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