Integral Calculus Question 200
Question: Let $ f:(0,\infty )\to R $ and $ F(x)=\int\limits_0^{x}{f(t)dt} $ .If $ F(x^{2})=x^{2}(1+x), $ then $ f(4) $ equals
Options:
A) $ \frac{5}{4} $
B) 7
C) 4
D) 2
Show Answer
Answer:
Correct Answer: C
Solution:
[c] $ F’(x)=f(x) $ Also, $ F(t)=t( 1+\sqrt{t} ) $
$ \Rightarrow F’(t)=1+\frac{3}{2}{t^{1/2}};F’(4)=1+3=4\Rightarrow f(4)=4 $
BETA
