Integral Calculus Question 25
Question: Correct evaluation of $ \int_{{}}^{{}}{\frac{x}{(x-2)(x-1)}\ dx} $ is
[MP PET 1993]
Options:
A) $ {\log_{e}}|\frac{{{(x-2)}^{2}}}{(x-1)}|+p $
B) $ {\log_{e}}|\frac{(x-1)}{(x-2)}|+p $
C) $ \frac{x-1}{x-2}+p $
D) $ 2{\log_{e}}|( \frac{x-2}{x-1} )|+p $ (where p is an arbitrary constant)
Show Answer
Answer:
Correct Answer: A
Solution:
$ \int_{{}}^{{}}{\frac{x}{(x-2)(x-1)},dx}=-\int_{{}}^{{}}{\frac{1}{x-1},dx+\int_{{}}^{{}}{\frac{2}{x-2},dx}} $ $ =-|{\log_{e}}(x-1)+2{\log_{e}}(x-2)|+c={\log_{e}}\frac{{{(x-2)}^{2}}}{(x-1)}+p. $
BETA
