Finding the Area of a Polar Region In Exercises 103-108, use a graphing utility to graph the polar equation. Find the area of the given region analytically.
Common interior of and
To calculate: The area of the region analytically. Also graph the common interior of the polar equation and using a graphing utility.
The polar equations are and .
Consider the equations, and .
Draw the graph of the equations, and using Ti83 calculator. The following steps are needed.
Step 1. Press on button.
Step 2. Press MODE button and choose ‘funct” and in funct choose Pol.
Step 3. Press button and write and
Step 4. Press GRAPH button.
And the graph of the polar equation and is obtained as below:
The area of the region between the circle between and is
Apply the limits with the help of the property:
The area of the region between the circle and can be obtained by integrating from and is:
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