Definite-Integration Question 527
Question: If $ F(x)=\frac{1}{x^{2}}\int_4^{x}{(4t^{2}-2{F}’(t)),dt,} $ then $ {F}’(4) $ equals
Options:
A) 32
B) $ \frac{32}{3} $
C) $ \frac{32}{9} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
We have $ F(x)=\frac{1}{x^{2}}\int_4^{x}{(4t^{2}-2F’(t))dt} $
$ \therefore F’(x)=\frac{1}{x^{2}}( 4x^{2}-2F’(x) )-\frac{2}{x^{3}}\int_4^{x}{(4t^{2}-2F’(t))dt} $
Þ $ F’(4)=\frac{1}{16}[64-2F’(4)]-0\Rightarrow F’(4)=\frac{32}{9} $ .
BETA
