Definite Integration Question 385
Question: If $ \int_0^{t^{2}}{xf(x)dx=}\frac{2}{5}t^{5},t>0, $ then $ f( \frac{4}{25} )= $
[IIT Screening 2004]
Options:
A) $ \frac{2}{5} $
B) $ \frac{5}{2} $
C) $ -\frac{2}{5} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ \int_0^{t^{2}}{xf(x)dx=\frac{2}{5}t^{5},t>0} $
Differentiate both sides w.r.t. t, we get $ t^{2}f(t^{2})2t=2t^{4} $
therefore $ f(t^{2})=t $
Put $ t=\frac{2}{5}, $ we get $ f( \frac{4}{25} )=\frac{2}{5} $ .
BETA
