The value of integral $\mathop \smallint \nolimits_0^\pi \,\,x\;\,\,f(\sin \,\,x)\;\,\,dx\,\,\;{\rm{is}}$

$\pi \,\mathop \smallint \nolimits_0^{\pi /2} \,\,f\;(\sin \,\,x)\;\,dx$

$\frac{\pi }{4}\,\,\mathop \smallint \nolimits_0^\pi \,\,f\;(\sin \,\,x)\;\,dx$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

The value of integral

\int \nolimits_0^\pi \,\,x\;\,\,f(\sin \,\,x)\;\,\,dx\,\,\;\mathrm{is}

View answer and explanation

Correct option: B

\pi \,\int \nolimits_0^{\pi /2} \,\,f\;(\sin \,\,x)\;\,dx

Option B (

\pi \,\int \nolimits_0^{\pi /2} \,f\;(\sin \,x)\,dx

) is correct because it uses the property of definite integrals to simplify the expression.

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