$\int x^2 \sin x d x$

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Indefinite Integration

Question:

$\int x^2 \sin x d x$

Options:

$x^2 \sin x-2 x \cos x+c$

$x^2 \sin x+c$

$-x^2 \cos x+2 x \sin x+2 \cos x+c$

$-x^2 \sin x-2 x \cos x+\sin x+c$

Correct Answer:

$-x^2 \cos x+2 x \sin x+2 \cos x+c$

Explanation:

By parts

$I=-x^2 \cos x+2 x \sin x+2 \cos x+c$ with alternate +, – sign.

Hence (3) is the correct answer.