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int(-pi/3)^0[cot^(-1)(2/(2cosx-1))+cot^(...

`int_(-pi/3)^0[cot^(-1)(2/(2cosx-1))+cot^(-1)(cosx-1/2)]dx` i s equal to (a)`(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`

Text Solution

Verified by Experts

The correct Answer is:
A
For `x epsilon(-(pi)/3,0),2 cos x-1gt0`
`:.I=int_(-pi//3)^(pi)//2 dx=(pi^(2))/6`
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CENGAGE-DEFINITE INTEGRATION -Exercise (Single)
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