A) \[9\]
B) \[3\]
C) \[\frac{1}{9}\]
D) \[\frac{1}{3}\]
Correct Answer: A
Solution :
Given, \[k\int_{0}^{1}{x.f(3x)}dx=\int_{0}^{3}{t.f(t)\,dt}\] ...(i) Let \[I=k\int_{0}^{1}{x\,f(3x)\,dx}\] Let \[3x=t\] \[\Rightarrow \] \[dx=\frac{dt}{3}\] when \[x=0,t=0\] when \[x=1,t=3\] \[\therefore \] \[I=k\int_{0}^{3}{\frac{t}{3}.f(t).\frac{dt}{3}}\] \[=\frac{k}{9}\int_{0}^{3}{f(t)\,dt}\] Now, from Eq. (i), we get \[\frac{k}{9}\int_{0}^{3}{t.\,f(t)\,dt=\int_{0}^{3}{t.f(t)\,dt}}\] \[\Rightarrow \] \[\frac{k}{9}=1\]\[\Rightarrow \]\[k=9\]
You need to login to perform this action.
You will be redirected in
3 sec
