Triple integrals can be evaluated in six different orders. There are six ways to express an iterated triple integral. While the function ???f(x,y,z)??? inside the integral always stays the same, the order of integration will change
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If the solid W is a cube defined by a ≤ x ≤ b, c ≤ y ≤ d, and p ≤ z ≤ q, then we can easily write the triple integral as an iterated integral. We could first integrate x from a to b, then integrate y from c to d, and finally integrate z from p to q , ∭
But triple integrals can be used to 1) find volume, just like the double integral, and to 2) find mass, when the volume of the region we’re interested in has variable density. In this
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The notation for the general triple integrals is, ∭ E f (x,y,z) dV ∭ E f ( x, y, z) d V Let’s start simple by integrating over the box, B = [a,b]×[c,d]×[r,s] B = [ a, b] × [ c, d] × [ r, s] Note
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But I want to do this example, just so that you get used to what a triple integral looks like, how it relates to a double integral, and then later in the next video we could do
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