18 - COM2

# 18 - COM2 - y = x 2 Let δ 1 Ex Let R be the lamina with...

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Center of Mass continued Divide the region into n strips parallel to the y-axis. Assume the center of mass of each sub-rectangle is at its geometric center. m i δ x i ) A i δ x i ) is the density of the ith rectangle. A i is the area of the ith rectangle. Since we are only going to consider constant density, δ x i ) δ .

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x δ x ( f ( x ) - g ( x )) dx a b δ ( f ( x ) - g ( x )) dx a b y 1 2 δ f ( x ) 2 - g ( x ) 2 dx a b δ ( f ( x ) - g ( x )) dx a b Suppose we integrate over the y-axis. x 1 2 δ f ( y ) 2 - g ( y ) 2 dy c d δ f ( y ) - g ( y ) dy c d y δ y ( f ( y ) - g ( y )) dy c d δ f ( y ) - g ( y ) dy c d
Ex. Find the center of mass of the region bounded by y = 2x and

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Unformatted text preview: y = x 2 . Let δ 1. Ex. Let R be the lamina with density 1 3 in the region in the xy plane bounded by y 4 x ,±± x 2,±± y 1 4 . Do. Let R be the lamina with density 2 in the region of the xy plane bounded by y ≥ 0, x ≥ 0, and y = 3 – 2x 2 . Set up integrals in both dx and dy to find M x and M y ....
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