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A definite Integral

Calculus (Integrals, Series)
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mathofusva
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A definite Integral

#1

Post by mathofusva » Fri Jun 15, 2018 7:55 pm

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
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Re: A definite Integral

#2

Post by Riemann » Tue Jun 19, 2018 7:20 pm

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
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Re: A definite Integral

#3

Post by mathofusva » Wed Jun 20, 2018 2:11 pm

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