If `kint_(0)^(1)xf(3x)dx=int_(0)^(3)tf(t)dt`, then the value of k isA. 9B. 3C. `1/9`D. `1/3`

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

1.	If `kint_(0)^(1)xf(3x)dx=int_(0)^(3)tf(t)dt`, then the value of k isA. 9B. 3C. `1/9`D. `1/3`
Answer» Correct Answer - A Let `l=kint_(0)^(1)xf(3x)dx` Put 3x=t `rArrdx=(dt)/(3)` `thereforel=kint_(0)^(3)(t)/(3)f(t)(dt)/(3)=(k)/(9)int_(0)^(3)tf(t)dt` Now `(k)/(9)int_(0)^(3)tf(t)dt=int_(0)^(3)t*f(t)dt` [ Given] `rArr(k)/(9)=1rArrk=9`

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