Let F : R\toR be a thrice differentiable function. Suppose that F(1) = 0, F(3) = -4 and F'(x) < 0 for all x ∊(1/2, 3). Let f (x) = xF(x) for all x ∊ R. If \int^{3}_{1}x^2F'(x)dx=-12 and \int^{3}_{1}x^3F"(x)dx=40,then the correct expression(s) is (are) [JEE Adv 2015 P2]

Application of Integration

Section: Mathematics

Question : 17 of 28

Marks: +1, -0

Let F:R→R be a thrice differentiable function. Suppose that F(1)=0, F(3)=−4 and F′(x)<0 for all x∊(

,3). Let f(x)=xF(x) for all x∊R.

If

∫

x2F′(x)dx=−12 and

∫

x3F"(x)dx=40,then the correct expression(s) is (are)

[JEE Adv 2015 P2]

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