The value of $\mathop \smallint \nolimits_0^{\pi /2} \,\,\frac{{{{(\sin \,\,x\,\, + \,\,\cos \,\,x)}^2}}}{{\sqrt {1\,\, + \,\,\sin \,\,2x} }}\,\,\;dx$ is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

The value of

\int \nolimits_0^{\pi /2} \,\,\frac{{{{(\sin \,\,x\,\, + \,\,\cos \,\,x)}^2}}}{{\sqrt {1\,\, + \,\,\sin \,\,2x} }}\,\,\;dx

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Correct option: C

\mathrm{2}

Option C (2) is correct because the integral simplifies to the integral of (sin x + cos x) from 0 to pi/2, which evaluates to 2.

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