integral of a function of two variables ƒ(x, y) over a region in theplane and the integral of a function of three variables ƒ(x, y, z)over a region in space. These integrals are called multiple integrals

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sketch the region of integration and write an equivalent double integral with the order of integration reversed

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Moments of Inertia•A body’s first moments (Table 15.1) tell us about balance and about the torquethe body.•If the body is a rotating shaft, however, we are more likely to be interested inhow much energy is stored in the shaft or about how much energy it will take toaccelerate the shaft to a particular angular velocity.

•This is where the second moment or moment of inertia comes in.

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Moments of Inertia

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