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f(x)=int0^x f(t) dt=x+intx^1 tf(t)dt, th...

`f(x)=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
We have,
`underset(0)overset(x)intf(t)dt=x+underset(x)overset(1)int t f(t) dt`
`rArr underset(0)overset(x)intf(t)dt=x-underset(1)overset(x)int t f(t) dt`
`rArr underset(0)overset(x)intf(t)dt=x+underset(1)overset(x)int t f(t) dt=x`
Differentiating w.r.t to x, we get
`f(x)+xf(x)=1rArr f(x)=(1)/(x+1)rArr f(1)=(1)/(2)`
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OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Section I - Solved Mcqs
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  19. If x in[(4n+1)(pi)/(2),(4n+3)(pi)/(2)] and n in N, then the value of i...

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