Grade 12th passMagical Mathematics[Interesting Approach]
Evaluateintegrate (1/a+bcosx).dx limit 0 to p
Evaluateintegrate (1/a+bcosx).dx limit 0 to p
1 Answer
Arun Kumar
Hello Student,
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
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty
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