A definite Integral

Calculus (Integrals, Series)
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mathofusva
Posts: 33
Joined: Tue May 10, 2016 3:56 pm

A definite Integral

#1

Post by mathofusva »

Evaluate
$$\int_0^{\pi/2}\,\frac{x}{\sin x}\,\log(1 - \sin x)\,dx.$$
Last edited by mathofusva on Wed Jun 20, 2018 2:11 pm, edited 1 time in total.
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Riemann
Posts: 176
Joined: Sat Nov 14, 2015 6:32 am
Location: Melbourne, Australia

Re: A definite Integral

#2

Post by Riemann »

Are you sure about the upper limit? Should not it be $\frac{\pi}{2}$ ?
$\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^s}= \prod_{p \; \text{prime}}\frac{1}{1-p^{-s}}$
mathofusva
Posts: 33
Joined: Tue May 10, 2016 3:56 pm

Re: A definite Integral

#3

Post by mathofusva »

Thanks, Riemann. The Upper limit should be $\pi/2$.
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