jee-main 2022 Q74

jee-main · India · session1_27jun_shift2 Integration by Substitution Substitution to Compute an Indefinite Integral with Initial Condition

Let $f$ be a differentiable function in $\left( 0 , \frac { \pi } { 2 } \right)$. If $\int _ { \cos x } ^ { 1 } t ^ { 2 } f ( t ) d t = \sin ^ { 3 } x + \cos x$, then $\frac { 1 } { \sqrt { 3 } } f ^ { \prime } \left( \frac { 1 } { \sqrt { 3 } } \right)$ is equal to
(1) $6 - 9 \sqrt { 2 }$
(2) $6 + \frac { 9 } { \sqrt { 2 } }$
(3) $6 - \frac { 9 } { \sqrt { 2 } }$
(4) $3 + \sqrt { 2 }$

Let $f$ be a differentiable function in $\left( 0 , \frac { \pi } { 2 } \right)$. If $\int _ { \cos x } ^ { 1 } t ^ { 2 } f ( t ) d t = \sin ^ { 3 } x + \cos x$, then $\frac { 1 } { \sqrt { 3 } } f ^ { \prime } \left( \frac { 1 } { \sqrt { 3 } } \right)$ is equal to\\
(1) $6 - 9 \sqrt { 2 }$\\
(2) $6 + \frac { 9 } { \sqrt { 2 } }$\\
(3) $6 - \frac { 9 } { \sqrt { 2 } }$\\
(4) $3 + \sqrt { 2 }$

Paper Questions

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