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If intxf(x)dx=(f(x))/(2), then f(x) is e...

If `intxf(x)dx=(f(x))/(2),` then `f(x)` is equal to

A

`e^(x)`

B

`e^(-x)`

C

`logx`

D

`(e^(x^(2)))/(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `f(x)=(e^(x^(2)))/(2)`
`therefore" "int x.(e^(x^(2)))/(2)dx=int 2x.(e^(x^(2)))/(4)dx`
`"Put "x^(2)=t rArr 2xdx=dt`
`therefore" "int(e^(t))/(4)dt=(e^(t))/(4)+C=(1)/(2)((e^(x^(2)))/(2))+C`
Hence, `intx f (x)dx=(1)/(2)f(x)+C,`
When `f(x)=(e^(x^(2)))/(2)`
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