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.
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!
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