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