Math 211-03

11-28-2017

* [Surfaces of revolution]*

1. Find the area of the surface generated by revolving the curve for about the y-axis.

Since the curve is revolved about the y-axis, the radius is . The area is

2. Find the area of the surface generated by revolving from to about the x-axis.

, so the area is

3. Find the area of the surface generated by revolving , , about the x-axis.

Notice that this is just with the sign of the middle term changed. But was squared, so must be squared:

Thus,

Now , so the area is

4. Find the area of the surface generated by revolving the following curve about the y-axis:

Since the curve is revolved about the y-axis, . So the area is

*Strength doesn't come from physical capacity. It comes from
indomitable will.* - *Mahatma Gandhi*

Copyright 2017 by Bruce Ikenaga