Question

Sketch the graph of $y=|x+3|$ and evaluate the area under the curve $y=|x+3|$ above X-axis and between x=-6 to x=0.

Answer 1

$|x+3|$$=\{\begin{array}{c}-(x+3),ifx<-3\\ x+3ifx>-3\end{array}$
$={\int }_{-6}^{-3}-(x+3)dx+{\int }_{-3}^0(x+3)dx$

$=(-0+\frac{9}{2})+(\frac{9}{2}-0)=9sq.unit$.