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Let F : R rarr R be a thrice differenti...

Let `F : R rarr R` be a thrice differentiable function, Supose that `F(1) = 0, F(3) = -4` and `F'(x) lt 0` for all `x in (1//2//3)`. Let `f(x) = xF(x)` for all `x in R`.
If `underset(1)overset(3)int_(1)^(3) x^(2)F'(x) dx = -12` and `int_(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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