$\mathop \smallint \nolimits_0^{\rm{\pi }} \,\,\frac{{{\rm{\theta }}\,\,\sin \,\,{\rm{\theta }}}}{{1\,\, + \,\,{{\cos }^2}\,\,{\rm{\theta }}}}\,\,{\rm{d\theta }}$ is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

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Application +4 | -1

\int \nolimits_0^\mathrm{\pi } \,\,\frac{{\mathrm{\theta }\,\,\sin \,\,\mathrm{\theta }}}{{1\,\, + \,\,{{\cos }^2}\,\,\mathrm{\theta }}}\,\,\mathrm{d\theta }

is equal to

View answer and explanation

Correct option: D

\frac{{{\pi ^2}}}{4}

Option A (

\frac{{{\pi ^2}}}{4}

) is correct because the integral is evaluated using properties of definite integrals and trigonometric substitution.

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