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

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

The value of

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

View answer and explanation

Correct option: C

\frac{1}{2}

The correct answer is C (1/2) because the integrand is the derivative of a simple trigonometric function, allowing for direct evaluation using the fundamental theorem of calculus.

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