Math 140

Section 6.2 Part II

Formula for the Volume of a Solid of Revolution using the Washer Method when rotating around the x-axis or any horizontal axis:

Formula for the Volume of a solid of Revolution using the Washer Method when rotating around the y-axis or any vertical axis:

(The details for R(x), r(x), R(y) and r(y) will be discussed in class.)

In class examples:

1. Find the volume of the solid generated by rotating the region bounded by the curve and the line about the x-axis.

2. Find the volume of the solid generated by rotating the region bounded by and about

a. The y-axis (i.e. x = 0)

b. The line x = -2

3. Set up the integral (Do Not Evaluate) for the volume of the solid obtained by rotating the region bounded by y = 0, y = sin(x), about y = -2.

4. (#32 from 6.2 HW) Set up but do not evaluate an integral for the volume of the solid obtained by rotating the region bounded by and about x = 10.