Chapter 13: Q 35. (page 1039)
Let be triangular region with vertices
If the density at each point in is proportional to the square of the point’s distance from the -axis, find the mass of .
Short Answer
The mass of lamina is.
Chapter 13: Q 35. (page 1039)
Let be triangular region with vertices
If the density at each point in is proportional to the square of the point’s distance from the -axis, find the mass of .
The mass of lamina is.
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Get started for freeIn Exercises 61–64, let R be the rectangular solid defined by
Assume that the density of R is uniform throughout.
(a) Without using calculus, explain why the center of
mass is
(b) Verify that is the center of mass by using the appropriate integral expressions.
In Exercises 45–52, rewrite the indicated integral with the specified order of integration.
Exercise 41 with the order dy dx dz.
Let 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" ?
Let be an integrable function on the rectangular solid , and let Use the definition of the triple integral to prove that:
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