If $I = \mathop \smallint \nolimits_{ - \pi }^\pi \,\,\frac{{{e^{\sin x}}}}{{{e^{\sin x\;}} + \,\,{e^{ - {\rm{sinx}}}}}}\,\,dx$, then I equals

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

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Application +4 | -1

I = \int \nolimits_{ - \pi }^\pi \,\,\frac{{{e^{\sin x}}}}{{{e^{\sin x\;}} + \,\,{e^{ - \mathrm{sinx}}}}}\,\,dx

, then I equals

View answer and explanation

Correct option: C

\pi

Option C (

\pi

) is correct because using the property of definite integrals and adding the original integral to the transformed integral simplifies the expression to

\pi

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