But then if you wanted the full radius, you have to go another 2 to go to the center of our axis of rotation. Once again, if you just take a given y right over there, you evaluate the y, you get an x value. That x value will just give you this distance. If you want the full distance, you have to subtract negative 2 from that x value, which is essentially the same thing as adding 2 to get our full radius. So our radius as a function of y is this thing right over here. Substituting back into this, we can now write our definite integral for our volume. The volume is going to be equal to the definite integral from negative 1 to 3 of pi times our radius squared dy.