Let f: {R} \rightarrow {R} be a twice differentiable function such that f(2)=1. If {\F}(x)=x f(x) for all {\x} \in {R}, \int_{0}^{2} x {\F}^{'}(x) \dx=6 and \int_{0}^{2} x^2 F^{' '}(x) \dx=40, then F^{'}(2)+\int_{0}^{2} F(x) \dx is equal to: [28 Jan 2025 Shift 2]

Definite Integrals Part 3

Section: Mathematics

Question : 33 of 115

Marks: +1, -0

Let f:R⟶R be a twice differentiable function such that f(2)=1. If F(x)=xf(x) for all x∈R,

∫

xF′(x)‌dx=6 and

∫

x2F′′(x)‌dx=40, then F′(2)+

∫

F(x)‌dx is equal to:

[28 Jan 2025 Shift 2]

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