jee-main 2021 Q73

jee-main · India · session3_20jul_shift2 Indefinite & Definite Integrals Piecewise/Periodic Function Integration
If $[ x ]$ denotes the greatest integer less than or equal to $x$, then the value of the integral $\int _ { - \pi / 2 } ^ { \pi / 2 } [ [ x ] - \sin x ] \, d x$ is equal to:
(1) $- \pi$
(2) $\pi$
(3) 0
(4) 1
If $[ x ]$ denotes the greatest integer less than or equal to $x$, then the value of the integral $\int _ { - \pi / 2 } ^ { \pi / 2 } [ [ x ] - \sin x ] \, d x$ is equal to:\\
(1) $- \pi$\\
(2) $\pi$\\
(3) 0\\
(4) 1