_ ,2 ^ ,3 dx x^2 - x = - Vidyadip

MCQ

$\int_{\,2}^{\,3} {\frac{{dx}}{{{x^2} - x}} = } $

A
$\log (2/3)$
B
$\log (1/4)$
✓
$\log (4/3)$
D
$\log (8/3)$

✓

Answer

Correct option: C.

$\log (4/3)$

c
(c) $I = \int_2^3 {\frac{{dx}}{{{x^2} - x}}} $$ = \int_2^3 {\frac{{dx}}{{x\,(x - 1)}}} $

$ = \int_2^3 {\left[ {\frac{1}{{x - 1}} - \frac{1}{x}} \right]} \,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}$.

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