# Thread: area between curves

1. ## area between curves

find the area enclosed by the curves y= x^2 + 7 and y= 2x^2 +3

thanks

2. Equate the functionsto find the limits of integration.

Then we get:

$\displaystyle \int_{-2}^{2}\left[(x^{2}+7)-(2x^{2}+3)\right]dx$

3. Let $\displaystyle f(x)=x^2+7$ & $\displaystyle h(x)=2x^2+3.$

These curves intersect at $\displaystyle f(x)=h(x),$ this yields $\displaystyle [-2,2].$ We need to integrate a certain function in such interval. We have $\displaystyle f(x)\ge h(x),$ and so our integral is

$\displaystyle \int_{ - 2}^2 {\left\{ {\left( {x^2 + 7} \right) - \left( {2x^2 + 3} \right)} \right\}\,dx} ,$ which confirms galactus' result.

(Exploiting the symmetry saves time on calculations.)