Integration of (xcos x)dx/(1+cos x) with limits from 0 to 2pi.
ankur srivastava , 12 Years ago
Grade 12
Integral Calculus> definite-integration...
1 AnswersRinkoo Gupta
Last Activity: 11 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
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