And so the volume of what they're asking us, the volume of the solid generated when r is rotated, well, r is kind of the space in between f of x and g of x. So it's going to be, the volume is going to be the difference between these volumes. It's going to be this volume, this is kind of the outer volume, and we're gonna take out its hollow core. We're gonna hollow it out by subtracting out this volume. So the volume of that region is going to be the integral, I'll do this in a new color, integral from zero to 1 1⁄2 of pi times one minus f of x squared dx minus the integral from zero to 1 1⁄2 of pi times one minus g of x squared dx. And this is a completely valid answer, but you might want to simplify it. We have the same bounds of integration.