Solution:
The area of the region bounded by the curves $y=x^{2}+2$, $y=x$, $x=0$ and $x=3$ is represented by the shaded area OCBAO as
Therefore, Area of OCBAO = Area of ODBAO – Area of ODCO $=\int_{0}^{3}\left(x^{2}+2\right) d x-\int_{0}^{5} x d x$ $=\left[\frac{x^{3}}{3}+2 x\right]_{0}^{3}-\left[\frac{x^{2}}{2}\right]_{0}^{3}$ $=[9+6]-\left[\frac{9}{2}\right]$ $=15-\frac{9}{2}$ $=\frac{21}{2}$ units
Find the area of the region bounded by the curves $y=x^{2}+2$, $y=x$, $x=0$ and $x=3$.
Find the area of the region bounded by the curves $y=x^{2}+2$, $y=x$, $x=0$ and $x=3$.