jee-main 2025 Q4

jee-main · India · session1_23jan_shift2 Integration by Parts Definite Integral Evaluation by Parts
Let $\int x ^ { 3 } \sin x \mathrm {~d} x = g ( x ) + C$, where $C$ is the constant of integration. If $8 \left( g \left( \frac { \pi } { 2 } \right) + g ^ { \prime } \left( \frac { \pi } { 2 } \right) \right) = \alpha \pi ^ { 3 } + \beta \pi ^ { 2 } + \gamma , \alpha , \beta , \gamma \in Z$, then $\alpha + \beta - \gamma$ equals :
(1) 48
(2) 55
(3) 62
(4) 47
Let $\int x ^ { 3 } \sin x \mathrm {~d} x = g ( x ) + C$, where $C$ is the constant of integration. If $8 \left( g \left( \frac { \pi } { 2 } \right) + g ^ { \prime } \left( \frac { \pi } { 2 } \right) \right) = \alpha \pi ^ { 3 } + \beta \pi ^ { 2 } + \gamma , \alpha , \beta , \gamma \in Z$, then $\alpha + \beta - \gamma$ equals :\\
(1) 48\\
(2) 55\\
(3) 62\\
(4) 47