Definite Integration Question 192
Question: $ \int _{2}^{3}{\frac{dx}{x^{2}-x}=} $
[EAMCET 2002]
Options:
A) $ \log (2/3) $
B) $ \log (1/4) $
C) $ \log (4/3) $
D) $ \log (8/3) $
Show Answer
Answer:
Correct Answer: C
Solution:
$ I=\int_2^{3}{\frac{dx}{x^{2}-x}} $
$ =\int_2^{3}{\frac{dx}{x(x-1)}} $
$ =\int_2^{3}{[ \frac{1}{x-1}-\frac{1}{x} ]}dx $
$ =\int_2^{3}{\frac{1}{(x-1)}}dx-\int_2^{3}{\frac{1}{x}dx} $
$ =[\log (x-1)]_2^{3}-[\log x]_2^{3} $
$ =[\log 2-\log 1]-[\log 3-\log 2] $
$ =2\log 2-\log 3=\log \frac{4}{3} $ .
BETA
