JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

Let

f(x)

be a function satisfying

f(x)+f(\pi-x)=\pi^{2}

\forall \, x \in \mathbb{R}

. Then

\int\limits_{{0}}^{\pi} f(x) \sin x d x

is equal to

View answer and explanation

Correct option: C

\pi^{2}

The correct answer is C (

\pi^{2}

) because using the property of definite integrals and the given functional equation, the integral simplifies to

\pi^{2}

after substitution and simplification.

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