Page 60 - Calculus for the Clueless, Calc II

The surface of revolution about the x-axis (distance is y) is:

Parametric:

Polar form:

For the y-axis, x replaces y and θ sin θ is replaced by θ cos θ.

Let us do one simple example, one clever example, and one known result.

Example 15—

Example 16 (Clever, Very Clever)—

Pretty clever ???? Not when you have to see this for yourself, it isn't.