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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`.
`Ifint_(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

`int _(1) ^(3) f (x) dx =12`

C

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

D

`int _(1)^(3) f (x) dx =-12`

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The correct Answer is:
C, D
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