Question

The area bounded by $y=2-|2-x|;y=\frac{3}{|x|}is\frac{k-3ln3}{2},$ then k = ___

Answer 1

$y=\{\begin{array}{cc}x;& x<2\\ 4-x;& x\ge 2\end{array}andy=\{\begin{array}{cc}\frac{3}{x};& x>0\\ \frac{-3}{x};& x<2\end{array}$
Required area PQRSP = area PQRP + area PRSP
$=\left|{\int }_{\sqrt{3}}^2(x-\frac{3}{x})dx\right|+\left|{\int }_2^3\left(\right(4-x)-\frac{3}{x})dx\right|=\frac{4-3ln3}{2}sq.unit$