Asked by Joana
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!
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!
Answers
Answered by
Steve
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.
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.
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