jee-main 2024 Q68

jee-main · India · session2_04apr_shift2 Indefinite & Definite Integrals Accumulation Function Analysis

Let $f ( x ) = \int _ { 0 } ^ { x } \left( t + \sin \left( 1 - e ^ { t } \right) \right) d t , x \in \mathbb { R }$. Then, $\lim _ { x \rightarrow 0 } \frac { f ( x ) } { x ^ { 3 } }$ is equal to
(1) $- \frac { 1 } { 6 }$
(2) $\frac { 2 } { 3 }$
(3) $- \frac { 2 } { 3 }$
(4) $\frac { 1 } { 6 }$

Let $f ( x ) = \int _ { 0 } ^ { x } \left( t + \sin \left( 1 - e ^ { t } \right) \right) d t , x \in \mathbb { R }$. Then, $\lim _ { x \rightarrow 0 } \frac { f ( x ) } { x ^ { 3 } }$ is equal to\\
(1) $- \frac { 1 } { 6 }$\\
(2) $\frac { 2 } { 3 }$\\
(3) $- \frac { 2 } { 3 }$\\
(4) $\frac { 1 } { 6 }$

Paper Questions

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