JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

\left[ x \right]

is the greatest integer

\le x

then

{\pi ^2}\int\limits_0^2 {\left( {\sin \frac{{\pi x}}{2}} \right)(x - \left| x \right|} {)^{\left[ x \right]}}dx

is equal to

View answer and explanation

Correct option: B

4\left( {\pi - 1} \right)

Option B (

4(\pi - 1)

) is correct because the integral is evaluated by splitting the integration range and using the greatest integer function.

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