area between line and parabola

**larz** · June 11th 2009, 08:17 AM

How do you find the area of the region enclosed by the line y=2x+4 and the parabola y=4-x^2 in the xy-plane? Thank you

**alexmahone** · June 11th 2009, 08:23 AM

The line and the parabola intersect at the points where the x-coordinate is 0 and -2. (Obtained by solving the 2 equations.)

$Area=\int\limits_{-2}^{0}(4-x^2)-(2x+4) dx$
$=\int\limits_{-2}^{0} (-x^2 - 2x)dx$
$=-\frac{x^3}{3}-x^2 |$ (from -2 to 0)
$=0-(\frac{8}{3}-4)$
$=\frac{4}{3}$

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