Question

Find the area bounded by the lines $y=|x+1|$ and $y=2-|x|$.

Answer 1

$|x+1|=2-|x|$

$x=1=2-x$ if $x>0$

$x=\frac{1}{2}$

$y=\frac{3}{2}$
$|x+1|=2-|x|$

$-1-x=2+x$ if $x<0$

$2x=-3$

$x=\frac{-3}{2}$

$y=\frac{-1}{2}$
$AB=\sqrt{{\left(\frac{1}{2}\right)}^2+{\left(\frac{1}{2}\right)}^2}=\frac{1}{\sqrt{2}}$

$AD=\sqrt{{\left(\frac{3}{2}\right)}^2+{\left(\frac{8}{2}\right)}^2}=\frac{\sqrt{18}}{2}$
$Area=AB\times AD=\frac{\sqrt{18}}{2\sqrt{2}}=3$