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If intf(x)dx=2 {f(x)}^(3)+C , then f (x)...

If `intf(x)dx=2 {f(x)}^(3)+C` , then f (x) is

A

`(x)/(2)`

B

`x^(3)`

C

`(1)/(sqrt(x))`

D

`sqrt((x)/(3))`

Text Solution

Verified by Experts

The correct Answer is:
d
We have , `intf(x)dx=2{f(x)}^(3)+C`
Differentiating both seides W. r. to , x, we get
`f(x)=6 {f(x)}^(2)f' (x)`
`rArr 6 f(x) f' (x)=1`
`rArr 6 int f(x) f'(x) dx=int1 dx`
`rArr6 int f(x) d (f (x)) int1 . dx`
`rArr6xx({f(x)}^(2))/(2)=xrArr{f(x)}^(2)=(x)/(3)rArr f(x)=sqrt((x)/(3))`
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