1. The problem statement, all variables and given/known data Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. 2. Relevant equations [itex]y = x^2, x = y^2[/itex] about [itex] y = -1 [/itex] 3. The attempt at a solution I tried using both cylindrical and washer methods - but for cylindrical I couldn't figure out what the shell radius would be, so I switched to washer. [itex]\pi\int_0^1(x^2+1)^2 - (√x+1)^2 dx[/itex] [itex]\pi\int_0^1 x^4 + 2x^2 - x - 2√x dx[/itex] [itex]\pi(x^5/5 + (2x^3)/3 - x^2/2 - (4x[/itex]^3/2[itex]))/3)[/itex] [itex]\pi(1/5 + 2/3 - 1/2 - 4/3)[/itex] [itex]-29\pi/30[/itex] And I get a negative volume. Any ideas? EDIT: Ah. I just noticed I subtracted in the wrong order - would that fix it? Edit2: Also, would you mind helping me with using the cylindrical method for this? Because I wasn't able to narrow down the shell radius - there was always a little unknown portion.