Definite Integration Question 269
Question: If $ F(x)=\int _{x^{2}}^{x^{3}}{\log tdt,(x>0),} $ then $ {F}’(x)= $
[MP PET 2001]
Options:
A) $ (9x^{2}-4x)\log x $
B) $ (4x-9x^{2})\log x $
C) $ (9x^{2}+4x)\log x $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ F(x)=\int _{x^{2}}^{x^{3}}{\log tdt} $
Applying Leibnitz-s theorem, $ F’(x)=\log x^{3}.\frac{d}{dx}x^{3}-\log x^{2}.\frac{d}{dx}x^{2} $
$ =3\log x.3x^{2}-2\log x.2x $
$ =(9x^{2}-4x)\log x $ .
BETA
