This question is killing me! :(
Find the total area of the regions enclosed by the relations x=y^3-y+1 and x=-y^3-y^2+1.
This is easiest if you integrate over y instead of x.
Thank you so much in advance!
It is certainly easier to integrate over y! Again, we have to distinguish between algebraic and geometric areas, since the curves cross each other at (1,0).
So, the area is
∫[-1,0] (-y^3-y^2+1)-(y^3-y+1) dy
+
∫[0,1/2] (-y^3-y^2+1)-(y^3-y+1) dy
Better double-check my math.