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

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

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Answer 1 · 2015-06-06T16:27:07

First let define the definite integral we need:
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So:
$\int_{- 3}^{1} (3 - 2 x - x^{2}) d x =$ $int_(-3)^(1)(3-2x-x^2)dx=$
$= {∣ ∣ ∣ 3 x - x^{2} - \frac{x^{3}}{3} ∣ ∣ ∣}_{- 3}^{2} =$ $=|3x-x^2-x^3/3|_(-3)^1=$
$= (3 - 1 - \frac{1}{3}) - (- 9 - 9 + \frac{27}{3}) =$ $=(3-1-1/3)-(-9-9+27/3)=$
$= \frac{5}{3} + 9 = \frac{32}{3}$ $=5/3+9=32/3$

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

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