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Integration of (xcos x)dx/(1+cos x) with limits from 0 to 2pi.

Integration of (xcos x)dx/(1+cos x) with limits from 0 to 2pi.

Grade:12

1 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
7 years ago
Solution :
integral of xcosx/(1+cosx)
=integral of x(cosx+1-1)/(1+cosx)
=integral of {x-x/(1+cosx)}dx
=x^2/2-integral of x/2cos^2(x/2) dx
=x^2/2 -1/2 integral x.sec^2(x/2) dx
integrating by part takin x as a first function and sec^(x/2) as a second function we get
x^2/2 -1/2 [ x.2tan(x/2) - intrgral of {1. 2tan(x/2) }dx
=x^2/2 -xtan(x/2)+ integral of tan(x/2) dx
=x^2/2-xtan(x/2)-2logmodcos(x/2) Ans.

Thanks & Regards
Rinkoo Gupta
AskIITians Faculty



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