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Definite Integration question

2021 · 31 Aug · Shift 2 · Q35

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PYQ Library
JEE Main
Mathematics
Definite Integration
2021 · 31 Aug · Shift 2 · Q35

Definite Integration question

2021 · 31 Aug · Shift 2 · Q35

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

If [x] is the greatest integer

\le

x, then

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

is equal to :

A
2( $\pi-$ 1)
B
4( $\pi-$ 1)
C
4( $\pi$ + 1)
D
2( $\pi$ + 1)

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