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pi-pi-sin-x-f-cos-x-dx-




Question Number 55773 by gunawan last updated on 04/Mar/19
 ∫_(−π) ^π  sin x f(cos x) dx =
$$\:\underset{−\pi} {\overset{\pi} {\int}}\:\mathrm{sin}\:{x}\:{f}\left(\mathrm{cos}\:{x}\right)\:{dx}\:= \\ $$
Answered by tanmay.chaudhury50@gmail.com last updated on 04/Mar/19
g(x)=sinxf(cosx)  g(−x)=−sinxf(cosx)  odd function  so ∫_(−π) ^π sinxf(cosx)dx=0
$${g}\left({x}\right)={sinxf}\left({cosx}\right) \\ $$$${g}\left(−{x}\right)=−{sinxf}\left({cosx}\right) \\ $$$${odd}\:{function} \\ $$$${so}\:\int_{−\pi} ^{\pi} {sinxf}\left({cosx}\right){dx}=\mathrm{0} \\ $$

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