Chapter 7: Additional Applications of Integration
Section 7.2: Integration in Polar Coordinates
Example 7.2.10
Obtain , the area element in polar coordinates.
Solution
In a circle, the central angle intercepts an arc of length . Taking the "wedge" shown in Figure 7.2.1 as a triangle, its area is half the base times the height. The base is the arc, approximated by and the altitude is approximated by , the length of either side of the angle . Hence, the area of the "wedge" in Figure 7.2.1 is taken as .
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