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The integral int(-pi//2)^(pi//2)(e^(|sin...

The integral `int_(-pi//2)^(pi//2)(e^(|sinx|).cosx)/(1+e^(tanx))dx` equals

A

e

B

`(e)/(2)`

C

`2e+1`

D

`e-1`

Text Solution

Verified by Experts

The correct Answer is:
D
`I=underset(0)overset(pi//2)(int)(e^(|sinx|)cosx)/(1+e^(tanx))+(e^(|sinx|)cosx)/(1+e^(-tanx))dx, " "I=underset(0)overset(pi//2)(int)e^(sinx).cosx dx`.
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