The value of the integral\\int_{-\\pi\/ 2} ^{\\pi\/ 2} {\sin ^{2} x}/{1+e^{x}} d xis

KVPY 2020-21 SB SX Exam Previous Papers

Question : 3 of 120

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The value of the integral

\∫↙{-\π\/ 2} ↖{\π\/ 2} {\sin ^{2} x}/{1+e^{x}} d x

Solution:

I=\∫↙{0} ↖{\π\/ 2}({\sin ^{2} x}/{1+e^{x}}+{\sin ^{2} x}/{1+e^{-x}}) d x

=\∫↙{0} ↖{\π\/ 2} \sin ^{2} x d x={1}/{2} \× {\π}/{2}={\π}/{4}

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