Question

Find the area of the region enclosed by parabola $y=x^2+2$ and lines $y=x,x=3$ and $x=0$

Answer 1

$y=x^2+2$ intersects Y-axis at $(0,2)$
Area of a region bounded by a Curve
$y=x^2+2$, line $y=x,x=3$ and $x=0$ is $A=\left|I\right|$
where $I={\int }_0^3(y_1-y_2)dx={\int }_0^3(x^2+2-x)dx={[\frac{x^3}{3}-\frac{x^2}{2}+2x]}_0^3=9+6-\frac{9}{2}$