# Area Between Curves?

## $y = {x}^{2}$ $y = 2 - {x}^{2}$ $y = 2 x + 8$

Jun 14, 2018

$= \frac{100}{3}$ Squared Units

#### Explanation:

by checking the graph You see you want the area surrounded by the three curves.

First, you get the points of intersection of,

color(green)((1)straight line and the curve $y = {x}^{2}$

$\left(- 2 , 4\right) , \left(4 , 16\right)$

color(green)((2) the two curves

$\left(- 1 , 1\right) , \left(1 , 1\right)$

First, You get the area between the straight line and the curve ${x}^{2}$ and then subtract from it the area between the two curves

color(green)("Area"=int_a^b(y_2-y_1)dx

Substitute with the given functions

Area $= {\int}_{-} {2}^{4} \left(2 x + 8 - {x}^{2}\right) \mathrm{dx} - {\int}_{-} {1}^{1} \left(2 - {x}^{2} - {x}^{2}\right) \mathrm{dx}$

$= \left({\left[{x}^{2} + 8 x - {x}^{3} / 3\right]}_{-} {2}^{4}\right)$

$- \left({\left[2 x - \frac{2 {x}^{3}}{3}\right]}_{-} {1}^{1}\right)$

$= \frac{100}{3}$ Squared Units