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Evaluate: int0^(2pi)1/(1+e^(sin x))dx...

Evaluate: `int_0^(2pi)1/(1+e^(sin x))dx`

Text Solution

Verified by Experts

I=`int_0^(2pi)1/(1+e^(sinx))dx....(1)`
I=`int_0^(2pi)1/(1+e^(sin(pi-x)))dx`
I=`int_0^pi e^sinx/(1+e^(sin(x)))dx...(2)`
(1)+(2)
2I=`int_0^(2pi)(1+e^(sin(x)))/(1+e^(sin(x)))dx`
`2I=[x]_0^(2pi)`
=`π`
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