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Let F : R to R be a thrice differentia...

Let F : R `to` R be a thrice differentiable function . Suppose that `F(1)=0,F(3)=-4 and F(x) lt 0 ` for all `x in (1,3)`. `f(x) = x F(x)` for all `x inR`.
If `int_(1)^(3)x^(2)F'(x)dx=-12 andint_(1)^(3)x^(3)F'' (x)dx =40`, then the correct expression (s) is //are

A

`9f'(3) + f'(1) - 32 = 0`

B

`underset(1)overset(3)intf(x)dx = 12`

C

`9f'(3) - f'(1) + 32 = 0`

D

`underset(1)overset(3)intf(x)dx = -12`

Text Solution

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The correct Answer is:
CD
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