Find the area of bounded by f(x)=2x^2
and g(x)=x^4-2x^2
First of all, find where the two curves intersect.
f(x) = g(x) where 2x^2 = x^4 -2x^2
4x^2 = x^4
x^2 = +/- 2x
x = -2, 0 and +2
Because of symmetry, you can integrate f-g = 4x^2 +x^4 from 0 to 2 and double the result.