Page 59 - Calculus for the Clueless

Example 14—

Find the area inside both the circle and the cardioid.

Now we know your instructor would never give such a problem, but .... This is a split region at the rays 0 =
±π/3. Region I is a sector of the circle. Region 2 is the "top" of the heart, the cardioid. So we get

Please note that polar coordinates are really not hard. It is just that many instructors rush through this section.
This makes this section appear difficult. It really is not.

Arc Length and Surface Area of Revolution

The derivations are in most books. All that remains is memorizing the formulas and applying them.

The arc length is:

or, in parameters: