Definite Integration Question 56
Question: $ \int _{1}^{x}{\frac{\log x^{2}}{x}dx=} $
[DCE 1999]
Options:
A) $ {{(\log x)}^{2}} $
B) $ \frac{1}{2}{{(\log x)}^{2}} $
C) $ \frac{\log x^{2}}{2} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ I=\int_1^{x}{\frac{2\log x}{x}dx} $
Let $ \log x=t $
therefore $ \frac{dx}{x}=dt $
$ \therefore I=2\int_0^{\log x}{tdt=2[ \frac{t^{2}}{2} ]}_0^{\log x}={{(\log x)}^{2}} $ .
BETA
