The value of $\mathop \smallint \nolimits_0^{\pi /2} \,\,\frac{{{2^{{\rm{sin}}x}}}}{{{2^{{\rm{sin}}x}} + \,\,{2^{{\rm{cos}}x}}}}\;\,\,dx$ is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

The value of

\int \nolimits_0^{\pi /2} \,\,\frac{{{2^{\mathrm{sin}x}}}}{{{2^{\mathrm{sin}x}} + \,\,{2^{\mathrm{cos}x}}}}\;\,\,dx

View answer and explanation

Correct option: C

\mathrm{\pi }/4

Option C (

\mathrm{\pi }/4

) is correct because it is obtained by using the property of definite integrals and adding two forms of the integral to simplify and solve.

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