Mathematics

Mathematics

Problem

Let ∫x3sin⁡x dx=g(x)+C\int x^3 \sin x \, dx = g(x) + C , where CC is the constant of integration. If 8(g(π2)+g′(π2))=απ3+βπ2+γ8(g(\frac{\pi}{2}) + g'(\frac{\pi}{2})) = \alpha\pi^3 + \beta\pi^2 + \gamma , α,β,γ∈Z\alpha, \beta, \gamma \in \mathbb{Z} , then α+β−γ\alpha + \beta - \gamma equals : A 48 B 55 C 62 D 47

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