let's find where the two curves intersects each other:
f(x) = x3 + x2 = x2 ( x + 1)
g(x) = 2x2 + 2x = 2x( x + 1)
f(x) = g(x) ===> x2 ( x + 1) = 2x( x + 1)
===> x(x+1) ( x - 2) = 0 ===> x = 0 ; x = -1 and x = 2
f(0) = 0
f(-1) = -1 + 1 = 0
f(2) = 23 + 22 = 8 + 4 = 12
we have the intersection points ( 0 , 0 ) ; (-1 , 0) and (2, 12 )
when -1 < x < 0 we have f(x) - g(x) > 0 ----> f is over g
when 0 < x < 2 we have f(x) - g(x) < 0 ----> f is under g
thus :
hope this helps