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Calculating Volume Using Double Integration Method

Learn how to find the volume under a surface within specific boundaries using double integration with clear examples and explanations.

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Calculating Volume Using Double Integration Method

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  1. Double Integration Greg Kelly, Hanford High School, Richland, Washington

  2. Find the volume under this surface between 0<x<2 and 0<y<1.

  3. z 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). y x

  4. z The volume of the slice is area . thickness y x We could hold x constant and take a slice through the shape. The area of the slice is given by:

  5. z y x We can add up the volumes of the slices by:

  6. with triangular base between the x-axis, x=1 and y=x. y x slice The base does not have to be a rectangle: thickness of slice area of slice Add all slices from 0 to 1.

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