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## Homework Statement

Given x=y^2, x=1 what is the area of the solid when the area between the two curves is rotated about x=1.

## The Attempt at a Solution

I attached my solution and according to the answer key my area formula (pi-pi*y^4) is wrong. Instead they have pi*(1-y^2)^2. Can anyone explain why my area formula is wrong? I thought that it was the area of the upper boundary curve minus the area of the lower boundary curve...