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If f(x)=1+1/x int1^x f(t) dt, then the...

If `f(x)=1+1/x int_1^x f(t) dt,` then the value of `f(e^-1)` is

A

`1`

B

`0`

C

`-1`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Given `xf(x)=x+int_(1)^(x)f(t)dt`…………….1
`f(x)+xf'(x)=1+f(x)`
`=f'(x)=1/x`
or `f(x)=log|x|+c`
`f(1)=1`
or `f(x)=log|x|+1`
or `f(e^(-1))=0`
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