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If int f(x)dx=F(x), then intx^3f(x^2)dx ...

If `int f(x)dx=F(x),` then `intx^3f(x^2)dx` is equal to :

A

`(1)/(2)[x^(2){F(x)}^(2)-int{F(x)}^(2)dx]`

B

`(1)/(2)[x^(2)F(x^(2))-intF(x^(2))d(x^(2))]`

C

`(1)/(2)[x^(2)F(x)-(1)/(2)int{F(x)}^(2)dx]`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
b
We have , `intf(x)dx=F(x)`.
`thereforeI=intx^(3)f(x^(2))dx=(1)/(2)intunderset(I)(x^(2))f(x^(2))underset(II" ")(d(x^(2)))`
`rArrI=(1)/(2)[x^(2)F(x^(2))=intF(x^(2))d(x^(2))]`
`rArrI=(1)/(2)[x^(2)F(x^(2))-intF(x^(2))d(x^(2))]`
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