If $I=\int\limits_0^\pi x \sin x d x$, t

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Definite Integration

Question:

If $I=\int\limits_0^\pi x \sin x d x$, then

Options:

$I=-\pi$

$I=2 \pi$

$I=2$

$I=\pi$

Correct Answer:

$I=\pi$

Explanation:

The correct answer is Option (4) - $I=\pi$

$I=\int\limits_0^\pi x \sin x d x$ ...(1)

$I=\int\limits_0^\pi (\pi - x)\sin (\pi - x)dx$

$I=\int\limits_0^\pi (\pi - x)\sin xdx$ ...(2)

adding (1) and (2)

$⇒2I=\pi\int\limits_0^\pi \sin xdx$

$⇒2I=\pi[\cos x]_0^\pi$

$2I=\pi×2$

$I=\pi$