Question

The area bounded by $y=2-|2-x|$ and $y=\frac{3}{|x|}$ is:

• A. $\frac{4+3\ln 3}{2}$
• B. $\frac{4-3\ln 3}{2}$
• C. $\frac{3}{2}+\ln 3$
• D. $\frac{1}{2}+\ell \ln 3$

Answer 1

Answer: (B)

$A=\underset{\sqrt{3}}{\overset{2}{\int }}\left(x-\frac{3}{x}\right)dx+\underset{2}{\overset{3}{\int }}\left(4-x-\frac{3}{x}\right)dx$
$={\left(\frac{x^2}{2}-3\ell \ln x\right)}_{\sqrt{3}}^2+{\left(4x-\frac{x^2}{2}-3\ell nx\right)}_2^3$

$=\frac{4-3\ln 3}{2}$