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Home Multiple Integrals Application to Physics Examples Example 1: Mass and Density
 
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Example 1: Mass and Density

Find the mass of an object in the shape of a unit square whose density is the sum of the distance from one edge and twice the distance from a second perpendicular edge.

Step 1

The region D is shown in Figure 12.4.2.

 

12_multiple_integrals-209.gif

Figure 12.4.2

Step 2

Place the object so the first two edges are on the x and y axes.

Then D is the region

0 ≤ x ≤ 1, 0 ≤ y ≤ 1.

Step 3

The density is ρ(x, v) = y + 2x.

12_multiple_integrals-210.gif

12_multiple_integrals-211.gif

Home Multiple Integrals Application to Physics Examples Example 1: Mass and Density

Last Update: 2006-11-15