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

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

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

is equal to

View answer and explanation

Correct option: C

- \,\,\frac{\pi }{2}\,\,\log \,\,2

Option C

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

is correct because by using the property

\int \nolimits_0^{a} f(x) dx = \int \nolimits_0^{a} f(a-x) dx

and trigonometric identities, the integral evaluates to

-\frac{\pi}{2}\log 2

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