Question

The shaded region represented in the diagram is rotated about the x- axis through 360degrees. Find the volume of the solid generated?

Answer 1

\[\Pi \int\limits_{0}^{2} x(x-2) dx\]

Answer 2

If you cut the solid into perpendicular cross-sections each section will be a circle with radius |x(x-2)| .
The Area of the cross-section would be pi*[x(x-2)]^2
volume is just the sum of each Area times dx

\[V = \pi \int\limits_{0}^{2}[x(x-2)]^{2} dx\]

Answer 3

Oops, I left off the squared...sorry

Answer 4

yeah thats what i figured :)