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Evaluate integrate (1/a+bcosx).dx limit 0 to p

Evaluate
integrate (1/a+bcosx).dx limit 0 to p

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3 Answers

Rinkoo Gupta
askIITians Faculty 81 Points
10 years ago
integrate dx/(a+bcosx)
put cosx=(1-tan^2(x/2))/(1+tan^(x/2))
integrate sec^2(x/2) dx/a(1+tan^2(x/2)+b(1-tan^2(x/2))
=integrate sec^2(x/2)dx/(a+b)+(a-b)tan^2(x/2)
put tan(x/2)=t
diff w. r. to x we get
sec^2(x/2).1/2 dx=dt
=integrate 2dt/(a+b)+(a-b)t^2
=2/sqrt(a+b) arctan( sqrt(a-b)t/sqrt(a+b))
=2/sqrt(a+b) arctan(sqrt(a-b)tan(x/2)/sqrt(a+b))
Thanks & Regards
Rinkoo Gupta
ASkIITians Faculty

Rohan
13 Points
4 years ago
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ankit singh
askIITians Faculty 614 Points
3 years ago
firstly you just change the cosx into half angel formula than u just put
tan(x/2)=t
diff w. r. to x we get
sec^2(x/2).1/2 dx=dt
=integrate 2dt/(a+b)+(a-b)t^2
=2/sqrt(a+b) arctan( sqrt(a-b)t/sqrt(a+b))
=2/sqrt(a+b) arctan(sqrt(a-b)tan(x/2)/sqrt(a+b))

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