jee-main 2021 Q75

jee-main · India · session1_25feb_shift1 Indefinite & Definite Integrals Piecewise/Periodic Function Integration
The value of $\int _ { - 1 } ^ { 1 } x ^ { 2 } e ^ { \left[ x ^ { 3 } \right] } d x$, where $[ t ]$ denotes the greatest integer $\leq t$, is :
(1) $\frac { e + 1 } { 3 }$
(2) $\frac { e - 1 } { 3 e }$
(3) $\frac { 1 } { 3 e }$
(4) $\frac { e + 1 } { 3 e }$ 
The value of $\int _ { - 1 } ^ { 1 } x ^ { 2 } e ^ { \left[ x ^ { 3 } \right] } d x$, where $[ t ]$ denotes the greatest integer $\leq t$, is :\\
(1) $\frac { e + 1 } { 3 }$\\
(2) $\frac { e - 1 } { 3 e }$\\
(3) $\frac { 1 } { 3 e }$\\
(4) $\frac { e + 1 } { 3 e }$
Paper Questions
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