Question

Using integration, find the area of the region bounded by the line $y-1=x$, the x-axis, and the ordinates $x=-2$ and $x=3$.

Answer 1

$\begin{array}{c}area=\underset{-2}{\overset{3}{\int }}(x+1)dx={\left[\frac{x^2}{2}+x\right]}_{-2}^3\\ =\frac{9}{2}+3-\left(\frac{4}{2}-2\right)=\frac{15}{2}.\end{array}$