Chapter 13: Q 32. (page 1039)
Let be triangular region with vertices
If the density at each point in is proportional to the point’s distance from the -axis, find the mass of .
Short Answer
The mass is
Chapter 13: Q 32. (page 1039)
Let be triangular region with vertices
If the density at each point in is proportional to the point’s distance from the -axis, find the mass of .
The mass is
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Get started for freeLet be a continuous function of three variables, let localid="1650352548375" be a set of points in the -plane, and let localid="1650354983053" be a set of points in -space. Find an iterated triple integral equal to the triple integral localid="1650353288865" . How would your answer change iflocalid="1650352747263" ?
Describe the three-dimensional region expressed in each iterated integral in Exercises 35–44.
Explain how to construct a midpoint Riemann sum for a function of three variables over a rectangular solid for which each is the midpoint of the subsolid role="math" localid="1650346869585" . Refer either to your answer to Exercise or to Definition .
In Exercises 57–60, let R be the rectangular solid defined by
R = {(x, y, z) | 0 ≤ x ≤ 4, 0 ≤ y ≤ 3, 0 ≤ z ≤ 2}.
Assume that the density ofR is uniform throughout.
(a) Without using calculus, explain why the center of mass is (2, 3/2, 1).
(b) Verify that the center of mass is (2, 3/2, 1), using the appropriate integral expressions.
Describe the three-dimensional region expressed in each iterated integral in Exercises 35–44.
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