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If int f(x)dx=f(x), then int {f(x)}^(2)d...

If `int f(x)dx=f(x)`, then `int {f(x)}^(2)dx` is equal to

A

`(1)/(2){f(x)}^(2)`

B

`{f(x)}^(3)`

C

`(|f(x)|^(3))/(3)`

D

`{f(x)}^(2)`

Text Solution

Verified by Experts

The correct Answer is:
a
We have , `intf(x)dx=f(x)rArr(d)/(dx)(f(x))=f(x)`
`rArr (1)/(f(x))d(f(x))-dx`
` rArr log(f(x))=x+logC`
`rArr f(x)=Ce^(x)`
`rArr {f(x)}^(2)=C^(2)e^(2x)`
`rArr int{f(x)}^(2)dx=intC^(2)e^(2x)dx=(C^(2)e^(2x))/(2)=(1)/(2){f(x)}^(2)`
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OBJECTIVE RD SHARMA ENGLISH-INDEFINITE INTEGRALS-Solved Example
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