Saved Bookmarks
| 1. |
Let I_(1)=int_(0)^(oo)ln(x+1/x)(dx)/(1+x^(2)) and l_(2)=int_(0)^(pi//2)((theta)/(sintheta))^(2)d theta, then which of the following is/are correct? |
|
Answer» `I_(1)gtI_(2)` `=[-theta^(2) cot theta]_(0)^(pi//2)+int_(0)^(pi//2) 2 theta cot theta d theta` Use: integration by parts `=- int_(0)^(pi//2)L nsin theta=pi l n 2` `I_(1)=int_(0)^(oo)ln(X+1/x)(dx)/(1+x^(2))` Let `tan^(-1)x = theta` `=int_(0)^(pi//2)l n (tan theta+cot theta) d theta` `=-int_(0)^(pi//2)(ln sin theta+l n cos theta) d theta=pi l N2` `:.I_(1)=I_(2)` |
|