# How do you find the area bounded by the curve y= 3-2x-x^2 and the x axis?

Jun 6, 2015

First let define the definite integral we need:

So:
${\int}_{- 3}^{1} \left(3 - 2 x - {x}^{2}\right) \mathrm{dx} =$
$= | 3 x - {x}^{2} - {x}^{3} / 3 {|}_{- 3}^{1} =$
$= \left(3 - 1 - \frac{1}{3}\right) - \left(- 9 - 9 + \frac{27}{3}\right) =$
$= \frac{5}{3} + 9 = \frac{32}{3}$