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Home Multiple Integrals Double Integrals in Polar Coordinates Examples Example 3
 
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Example 3

Find the moment of inertia of a circle of radius b and constant density ρ about the center of the circle.

Step 1

Draw the region D (Figure 12.5.11).

12_multiple_integrals-283.gif

Figure 12.5.11

Step 2

Put the origin at the center, so D is the polar region 0 ≤ 0 ≤ 2π, 0 ≤ r ≤ b.

Step 3

x2 + y2 = r2, so

12_multiple_integrals-282.gif

 
Home Multiple Integrals Double Integrals in Polar Coordinates Examples Example 3

Last Update: 2006-11-15