Calc11_5 DoubleIntegration

Calc11_5 DoubleIntegration - x y z We can add up the...

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Double Integration Greg Kelly, Hanford High School, Richland, Washington
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( 29 , 4 f x y x y = - - Find the volume under this surface between 0<x<2 and 0<y<1.
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x y z ( 29 , 4 f x y x y = - - 0 2 and 0 1 x y < < < < We can sketch the graph by putting in the corners where (x=0, y=0), (x=2, y=0), (x=0, y=1), (x=2, y=1).
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x y z We could hold x constant and take a slice through the shape. 1 0 4 x y dy - - The area of the slice is given by: The volume of the slice is area . thickness area dx =
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Unformatted text preview: x y z We can add up the volumes of the slices by: 2 1 4 x y dy dx- - 1 2 2 1 4 2 y xy y dx-- 2 1 4 2 x dx- - 2 2 1 1 4 2 2 x x x--5 8 2 1- - The base does not have to be a rectangle: ( 29 , 3 f x y x y = - -with triangular base between the x-axis, x=1 and y=x. x y slice 1 3 x x y dy dx- - area of slice thickness of slice Add all slices from 0 to 1....
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Calc11_5 DoubleIntegration - x y z We can add up the...

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