Volume by Integration: Disk Method Practice Problem Solution
3. Find the volume of y2 = 8x rotated about the x = 2 axis.
Now write the equation for the volume of the disk, dV= pr2dy.
The radius, r is not x. Looking at the sketch we see that r=2-x. So:
dV= p(2-x)2dy = p(2-y2/8)2dy
Now set up the integral. The limits are in the y direction at the end point of the object where x=2. Solving for y at x=2, we get +4 and -4.