6.3 Integral Applications
Question #3 (Medium): Finding Volume by Cylindrical Shells
First, graph the region bound by the function and the lines.
If the rotation is not typical or -axis, then measure from the line of rotation and modify the radius
If the height stretches vertically and the interval for integral moves across horizontally, the rotation is
about the -axis. Similarly, if the height lies horizontally and the interval for integral moves up vertically,
the rotation is about the -axis.
Substitute the appropriately expressed height and the radius into the integral using cylindrical shells to
calculate the volume: ∫ .
Using cylindrical shells find the volume obtain