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. 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

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

6. 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.