Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

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

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

Grade:

1 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
7 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

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free