2009-10-28: Triple Integrals
Stewart section 16.6
- Double Integrals add up a property
f(x,y) of a small area element dA
of a region R.
- Triple Integrals add up a property
f(x,y,z) of a small volume element dV
of a (3D) region E.
- Key Point
We set up triple integrals by reducing them to double and single
integrals.
- Example: Consider an overturned pyramid.
- Game:
- Set up the double integral over the region R in the
xy-plane.
- Find the limits on z
- Set up the triple integral for V
- Evaluate it to find V
- Game:
Now density d = (60 - z)/120
- Game:
Consider a corner planter bounded by z = 1,
z = 1 + x + y, in the first octant, with
density p = z.
- Set up an integral for the mass
- And for the x, y, and z coordinates
of the center of mass.
ma215-080-f09 lecture outline 2009-10-28
Created: Wed Oct 28 12:46:12 EDT 2009
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©2009 Gavin LaRose