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int(0)^(pi)(dx)/((1+sinx))=?...

`int_(0)^(pi)(dx)/((1+sinx))=?`

A

`(1)/(2)`

B

`1`

C

`2`

D

`0`

Text Solution

Verified by Experts

`I=int_(0)^(pi)((1-sinx))/((1-sin^(2)x))dx=int_(0)^(pi)((1-sinx))/(cos^(2)x)dx`
`=int_(0)^(pi)[sec^(2)x-secxtanx]dx=[tanx-secx]_(0)^(pi)=2`.
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