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If int(0)^(x) f ( t) dt = x + int(x)^(1)...

If `int_(0)^(x) f ( t) dt = x + int_(x)^(1) tf (t) dt `, then the value of f(1) is

A

`(1)/(2)`

B

0

C

1

D

`-(1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Given , `int_(0)^(x) f (t) = x + int_(x)^(1)t f (t) dt`
On differentiating both sides W . R. t. x , we get
`f(x)1 = 1x f (x) *1 rArr (1+x)f(x)=1`
`rArr f(x)=(1)/(1 +x)rArr f (1) =(1)/( 1 + 1)=(1)/(2)`
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