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If the function f:[0,8]vecR is different...

If the function `f:[0,8]vecR` is differentiable, then for `0

A

`3[alpha^(3)f(alpha^(2))+beta^(2)f(beta^(2))]`

B

`3[alpha^(3)f(alpha)+beta^(3)f(beta)]`

C

`3[alpha^(2)f(alpha^(3))+beta^(2)f(beta^(3))]`

D

`3[alpha^(2)f(alpha^(2))+beta^(2)f(beta^(2))]`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `g(xS)=int_(0)^(x^(3))f(t)dt`
Now, `int_(0)^(8)f(t)dt=g(2)=(g(2)-g(1))/(2-1)+(g(1)-g(0))/(1-0)`
`g'(alpha)+g'(beta)`
`=3[alpha^(2)f(alpha^(3))+beta^(2)f(beta^(3))]`
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