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If kint(0)^(1)xf(3x)dx=int(0)^(3)tf(t)dt...

If `kint_(0)^(1)xf(3x)dx=int_(0)^(3)tf(t)dt`, then the value of k is

A

9

B

3

C

`(1)/(9)`

D

`(1)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `l=kint_(0)^(1)xf(3x)dx`
Let `3x=t`
`impliesdx=(dt)/(3)`
`therefforel=kint_(0)^(3)(t)/(3)f(t)(dt)/(3)`
`=(k)/(9)int_(0)^(3)ft(t)dt`
Now, `(k)/(9)int_(0)^(3)tf(t)dt=int_(0)^(3)tf(t)dt`
`implies(k)/(9)=1impliesk=9`
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