Find the total area bounded?

Question

Find the total area bounded by the cubic x=y^3-y and the line x=3y. 

 

Answer: 8

 

Please show all your work. 

Answer 1

Sun 

 

         The line intersects the cubic at y=-2,0,2  so the area bounded by the two curves =∫(3y-y³+y)dy from y=-2 to y=2 which is 2*(2y²-y⁴/4) from 0 to 2 =2*(8-4)=8. So the area is 8 sq units.

 

Jim