L12b - Center of Mass of a Region Between Curves

# L12b - Center of Mass of a Region Between Curves - lamina...

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Divide center o m i where: x i  A i is Since w Cente the regi of mass   x i  is the de s the are we are on er of Ma ion into n of each A i ensity of ea of the nly goin ass of a (Se strips p sub-rect f the i th re i th rectan ng to con Region ction 6.7) parallel tangle is ectangle ngle. nsider co n Betwe ) to the y- s at its ge e. onstant d een Cur axis. A eometric density, rves ssume th c center. x i    he .

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x x ( f ( x ) g ( x )) dx a b ( f ( x ) g ( x )) dx a b y 1 2 f ( x ) 2 g ( x ) 2 dx a b ( f ( x ) g ( x )) dx a b Suppose we integrate over the y-axis. x 1 2 f ( y ) 2 g ( y ) 2 dy c d f ( y ) g ( y ) dy c d y y ( f ( y ) g ( y )) dy c d f ( y ) g ( y ) dy c d
Ex. Let R be the lamina with density 3 in the region in the xy plane bounded by x = e y , x = 1, and y = 2. Find the mass of the

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Unformatted text preview: lamina. Ex. Find the center of mass of the region bounded by y = 2x and y = x 2 . Let 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 . Find the center of mass of R by integrating w.r.t. y. 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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L12b - Center of Mass of a Region Between Curves - lamina...

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