Question

`int_(-pi/3)^0[cot^(-1)(2/(2cosx-1))+cot^(-1)(cosx-1/2)]dxi se q u a lto` `(pi^2)/6` (b) `(pi^2)/3` (c) `(pi^2)/8` (d) `(3pi^2)/8`
A. `(pi^(2))/6`
B. `(pi^(2))/3`
C. `(pi^(2))/8`
D. `(3pi^(2))/8`

Answer 1

Correct Answer - A
For `x epsilon(-(pi)/3,0),2 cos x-1gt0`
`:.I=int_(-pi//3)^(pi)//2 dx=(pi^(2))/6`