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int(0)^(1)(dx)/(e^(x)+e^(-x))...

`int_(0)^(1)(dx)/(e^(x)+e^(-x))`

A

`(1-(pi)/(4))`

B

`tan^(-1)e`

C

`tan^(-1)e+(pi)/(4)`

D

`tan^(-1)e-(pi)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
D
`I=int_(0)^(1)(dx)/((e^(x)+(1)/(e^(x))))=int_(0)^(1)(e^(x)dx)/((e^(2x)+1))=int_(0)^(e)(dt)/((t^(2)+1))`, where `e^(x)=t`.
`=[tan^(-1)t]_(1)^(e)=(tan^(-1)e-(pi)/(4))`.
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