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int(-1)^(1)(e^(x)+e^(-x))/(2(1+e^(2x)))d...

`int_(-1)^(1)(e^(x)+e^(-x))/(2(1+e^(2x)))dx` is equal to

A

0

B

1

C

`(e^(2)-1)/(2e)`

D

`(e^(2)+2)/(2e)`

Text Solution

Verified by Experts

The correct Answer is:
C
`int_(-1)^(1)(e^(x)+e^(-x))/(2(1+e^(2x)))dx`
`=1/2int_(-1)^(1)(1+e^(2x))/((1+e^(2x))e^(x))dx`
`=1/2int_(-1)^(1)e^(-x)dx=-1/2[e^(-x)]_(-1)^(1)`
`=-1/2(e^(-1)-e^(1))=(e^(2)-1)/(2e)`
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