lecture14 - Lecture 14 Applications of Double Integrals...

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Lecture 14: Applications of Double Integrals June 4, 2009 Lecture 14: Applications of Double Integrals
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Objectives 1 Given a density function, find the mass, center of mass, moments of intertia of a thin plate. 2 Given a probability distribution function, calculate probabilities and expected values. Lecture 14: Applications of Double Integrals
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Integral of density Suppose that we have a thin plate (lamina) described by a region R . Let ρ ( x , y ) be the density of the plate at a point ( x , y ). We define the mass to be m = Z Z R ρ ( x , y ) dA Lecture 14: Applications of Double Integrals
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Center of mass Suppose that we have a thin plate (lamina) described by a region R . Let ρ ( x , y ) be the density of the plate at a point ( x , y ). Lecture 14: Applications of Double Integrals
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Center of mass Suppose that we have a thin plate (lamina) described by a region R . Let ρ ( x , y ) be the density of the plate at a point ( x , y ). We define the moments to be M x = Z Z R y ρ ( x , y ) dA M y = Z Z R x ρ ( x , y ) dA Lecture 14: Applications of Double Integrals
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Center of mass
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