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 f(x, y, z) and g(x, y, z) be integrable functions on the rectangular solid . . Use the definition of the triple integral to prove that :
In Exercises 61–64, let R be the rectangular solid defined by
Assume that the density of R is uniform throughout.
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(b) Verify that is the center of mass by using the appropriate integral expressions.
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What is the difference between a triple integral and an iterated triple integral?
Find the masses of the solids described in Exercises 53–56.
The solid bounded above by the plane with equation 2x + 3y − z = 2 and bounded below by the triangle with vertices (1, 0, 0), (4, 0, 0), and (0, 2, 0) if the density at each point is proportional to the distance of the point from the
xy-plane.
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