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integrate (1/1-2acosx+a²).dx limit 0 to p

integrate (1/1-2acosx+a²).dx limit 0 to p

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Rinkoo Gupta
askIITians Faculty 81 Points
10 years ago
integral 1/(1-2acosx+a^2).dx lim 0 to pie
put cosx=(1-tan^(x/2))/(1+tan^(x/2))
integral sec^2(x/2)dx/(1+a^2)(1+tan^2(x/2))-2a(1-tan^2(x/2)) lim 0 to pie
put tan(x/2)=t
diff. w.r. to x , we get
1/2 sec^(x/2) dx=dt
=2 integral dt/(1-a^2)+(1+a^2)t^2 lim 0 to infinity
=2/(1-a) arctan((1+a)t/(1-a)) lim 0 to infinity
=2/(1-a) [arctan(infinity)-arctan(0)]
=2/(1-a).pie/2
=pie/(1-a)

Thanks & Regards
Rinkoo Gupta
AskIItians Faculty

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