JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int\limits_{{\pi / 3}}^{\pi / 2} x \sin (\pi[x]-x) d x

is equal to :

View answer and explanation

Correct option: B

1-\frac{\sqrt{3}}{2}+\frac{\pi}{6}

Option B (

1-\frac{\sqrt{3}}{2}+\frac{\pi}{6}

) is correct because in the interval

[\frac{\pi}{3}, \frac{\pi}{2}]

[x] = 1

, so the integral simplifies and can be evaluated using integration by parts.

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