Question

The integral $\underset{2}{\overset{4}{\int }}$ $\frac{log{x}^2}{log{x}^2+log\left(36-12x+x^2\right)}dx$ is equal to

• A. 2
• B. 4
• C. 1
• D. 6

Answer 1

Answer: (C)

$I=\underset{2}{\overset{4}{\int }}\frac{\log x^2}{\log x^2+\log (x-6{)}^2}dx\dots .(1)$
using $\underset{a}{\overset{b}{\int }}f(x)dx=\underset{a}{\overset{b}{\int }}f(a+b-x)dx$
$I=\underset{2}{\overset{4}{\int }}\frac{\log (6-x{)}^2}{\log (6-x{)}^2+\log x^2}dx\dots (2)$
$(1)+(2)$ gives
$2I=\underset{2}{\overset{4}{\int }}1dx=2$
$I=1$