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

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

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

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

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

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