JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

The value of

\int\limits_{0}^{4 / \pi}\left(3 x^2 \sin \frac{1}{x}-x \cos \frac{1}{x}\right) d x

is:

View answer and explanation

Correct option: C

\frac{32 \sqrt{2}}{\pi^3}

Option C (

\frac{{32 \sqrt{2}}}{\pi^3}

) is correct because after integration by parts, the limit as x approaches 0 of

x^3 \sin(1/x)

is 0, leading to the correct result.

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