Question

Find the area of the region that is enclosed between the curves y = x2 and
y = x + 6.

Answer 1

Integrate:

`\displaystyle\int_(-2)^3((x+6)-x^2)\,\mathrm dx = \int_(-2)^3(6+x-x^2)\,\mathrm dx`

`=\left(6x+\frac{x^2}2-\frac{x^3}3\right)\bigg|_(-2)^3`

`=\left(18+\frac92-9\right) - \left(-12+2+\frac83\right)`

`=\boxed{\frac{125}6}`