1. Calculate the volume of the solid obtained by revolving the region under the graph of f(x) = x + 1 about the x-axis over the interval [0, 3]. Draw a sketch of the solid.
2. Find the volume of the solid obtained by revolving the region under the graph of f(x) = x + 1 about the line y = -2 over the interval [0,3].
3. Calculate the volume of the solid obtained by rotating the region enclosed by the curves y = 2x and y = x^2 about the x-axis. Draw a sketch of the solid.
4. Graph the solid obtained by rotating the region enclosed by the graphs as indicated about the y-axis. Find the volume using discs. (3 pts)
y = x^2, y = 8 - x^2, x = 0, for x ≥ 0
5. Find the volume of the solid obtained in number 3 using cylindrical shells.