Mathematics
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ComplexYetTrivial
  • Member for 5 years, 5 months
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I am a physics student who, slightly frustrated by the neglect of rigour in physics, has decided to waste some time on mathematical technicalities. I like integrals.

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question
24
When is $\int_0^1 \int_0^1 \frac{f(x) - f(y)}{x-y} \, \text{d} x \, \text{d} y = 2 \int_0^1 f(t) \log\left(\frac{t}{1-t}\right) \, \mathrm{d} t$?
May 11, 2019
question
23
A closed form for $\int_0^\pi \lvert \sin(m t) \cos(n t) \rvert \, \mathrm{d} t$
Jul 22, 2018
question
22
Is there a set $A \subset [0,1]$ such that $\int_{A \times A^\text{c}} \frac{\mathrm{d} x \, \mathrm{d} y}{\lvert x - y\vert}=\infty$?
Apr 15, 2020
answer
21
Why is $ \int_0^{2\pi}\frac{\cos t - r}{1 - 2r\cos t + r^2}\,dt$ always zero for $r\in[0,1)$
Jan 26, 2019
answer
15
Checking whether $\int_{B(0,r)} \int_{B(0,r)} \ln(\|x-y\|)dxdy > 0$?
Feb 25, 2022
answer
14
Integral $\int_0^1 \frac{2x-1}{1+x-x^2}\left(4\ln x\ln(1+x)-\ln^2(1+x)\right)dx$
Oct 15, 2019
answer
14
Prove that $\lim_{t \to \infty} \int_1^t \sin(x)\sin(x^2)\,dx$ converges
Feb 14, 2020
answer
13
Integral ${\frac{1}{\pi^2}} \int_{0}^{\infty}\frac{{(\ln{x}})^2}{\sqrt{x}{(1-x)^2}} \mathrm d x$
Mar 6, 2019
question
13
Tied chess matches and the monotonicity of $\sum_{k=0}^n \binom{2n}{k,k,2n-2k} (pq)^k (1-p-q)^{2n-2k}$
Sep 26, 2021
answer
12
Trying to evaluate $\int_{0}^{\infty}\frac{\ln(1+x^3)}{1+x^3}\frac{dx}{1+x^3}$
Jul 10, 2018
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'The equation reads' or 'the equation reads as'?

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