Please show all work. Explanations are very helpful.
1. Find the volume of the solid formed by rotating the ellipse (x/a)^2 + (y/b)^2 = 1 about the x axis.
12. The base of a solid is the region bounded by the parabola y = x^2 / 2 and the line y = 2. Each plane section of the solid perpendicular to the y axis is an equilateral triangle. Find the volume of the solid.
17. Find the volume of the sphere by integrating from y = -r to y = r . Compare the result with the one arrived at by taking twice the integral from y = 0 to y = r.© BrainMass Inc. brainmass.com October 10, 2019, 1:35 am ad1c9bdddf
The expert finds the volume of solids in this case.