JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumIntegral Calculus369× since 2002Let ∫x3sinx dx=g(x)+C\int x^3 \sin x \, dx = g(x) + C∫x3sinxdx=g(x)+C, where CCC is the constant of integration. If 8(g(π2)+g′(π2))=απ3+βπ2+γ8\left(g\left(\frac{\pi}{2}\right) + g'\left(\frac{\pi}{2}\right)\right) = \alpha \pi^3 + \beta \pi^2 + \gamma8(g(2π)+g′(2π))=απ3+βπ2+γ, α,β,γ∈Z\alpha, \beta, \gamma \in \mathbb{Z}α,β,γ∈Z, then α+β−γ\alpha + \beta - \gammaα+β−γ equals:AOption A. 48BOption B. 55COption C. 62DOption D. 47CheckSkip · show solution
