Area enclosed by polar graphs

The Area enclosed by polar graphs exercise appears under the Integral Calculus Math Mission. This exercise shows you how to find the area between two graphs on a polar graph.

Types of Problems
There are two types of problems in this exercise: 1. Determine the area of the shaded region: The student is asked to find the area of the shaded region by taking integrals of the function.

2. Determine which integral evaluates to the area of the shaded region: The student is asked to select the integral that would evaluate to the area of the shaded region.

Strategies
Knowledge trigonometric integrals and polar graphs are encouraged to ensure success on this exercise.



1. Area of a polar graph = $$\frac{1}{2}\int r^2 d(\theta)$$

2. $$cos^2(theta)$$ = $$\frac{1}{2}(1+cos(2\theta))$$

3. $$sin^2(theta)$$ = $$\frac{1}{2}(1-cos(2\theta))$$

4. You can check your answer by evaluating the problem on a graphing calculator.