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Unformatted text preview: of 1 since this can be easily interpreted as the Volume of the Solid. This
assumption makes it easier to introduce the idea of a triple integral. Later we will have an integrand
have applications for it. Remember for a double integral we chopped up a region in the xy-plane (2D). For a triple
integral we will chop up a solid (a 3D region). So instead of having little rectangles we will have little cubes. Summing up
those cubes will give us an approximation of the volume of the solid.
We also want to be able to set up a triple integral with the different combinations of the order of integration. Just as we
learned to use dx dy and dy dx for a double integral, we will look at the combinations for a triple integral:
dz dy dx / dx dy dz / dy dz dx / dx dz dy etc. The best way to learn this is through an example: In Summary for calculating Area and Volume: Mass =
Summary of Section 13.5
1 Sketch the solid represented by a triple integral 2 Change the order of integration for a triple integral 3 Compute the Mass of a Solid with a triple integral 4 Evaluate a triple integral Section 13.6 Cylindrical Coordinates
This idea was introduced at the end of cha...
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