$\mathop \smallint \nolimits_0^{\pi /2} \,\,\log \,\,\sin \,\,x{\rm{ }}\,dx$ is equal to

$ - \,\left( {\frac{{\rm{\pi }}}{2}} \right)\,\,\log \,\,2$

${\rm{\pi }}\,\,\log \,\,\frac{1}{2}$

$ - \,{\rm{\pi }}\,\,\log \,\,\frac{1}{2}$

$\frac{{\rm{\pi }}}{2}\,\,\log \,\,2$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Analyzing +4 | -1

\int \nolimits_0^{\pi /2} \,\,\log \,\,\sin \,\,x\mathrm{ }\,dx

is equal to

View answer and explanation

Correct option: A

- \,\left( {\frac{\mathrm{\pi }}{2}} \right)\,\,\log \,\,2

Option A is correct because by using properties of definite integrals and trigonometric identities, the integral can be simplified and evaluated to

- \left( {\frac{\mathrm{\pi }}{2}} \right)\,\log \,2

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