Definite Integration Question 441

Question: The value of $ \int_1^{2}{\log xdx} $ is

[Roorkee 1995]

Options:

A) $ \log 2/e $

B) $ \log 4 $

C) $ \log 4/e $

D) $ \log 2 $

Show Answer

Answer:

Correct Answer: C

Solution:

$ \int_1^{2}{\log xdx=[x\log x-x]_1^{2}=2\log 2-2+1} $

$ =\log 4-1=\log 4-\log e=\log \frac{4}{e} $ .