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)

$A=\int\limits_{\sqrt{3}}^2\left(x-\frac{3}{x}\right) d x+\int\limits_2^3\left(4-x-\frac{3}{x}\right) d x$
$=\left(\frac{x^2}{2}-3 \ell \ln x\right)_{\sqrt{3}}^2+\left(4 x-\frac{x^2}{2}-3 \ell n x\right)_2^3$

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