Let ∫ x³ sin x dx = g(x) + C, where C is the constant of integrat… | JEE Main 2025 Mathematics PYQ

MCQMediumJEE Main 2025 · 23 January, Shift 2Integration Techniques (Substitution, Parts, Partial Fractions)

Let $\int x^3 \sin x \, dx = g(x) + C$ , where $C$ is the constant of integration. If $8\left( g\left( \frac{\pi}{2} \right) + g'\left( \frac{\pi}{2} \right) \right) = \alpha \pi^3 + \beta \pi^2 + \gamma, \quad \alpha, \beta, \gamma \in \mathbb{Z}$ , then $\alpha + \beta - \gamma$ equals:

A
$55$
B
$47$
C
$48$
D
$62$

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