Chapter 7: Additional Applications of Integration
Section 7.2: Integration in Polar Coordinates
Obtain dA=12r2dθ, the area element in polar coordinates.
In a circle, the central angle dθ intercepts an arc of length r dθ. 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 r dθ and the altitude is approximated by r, the length of either side of the angle dθ. Hence, the area of the "wedge" in Figure 7.2.1 is taken as 12r dθr=12r2dθ.
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