Chapter 13: Q.14 (page 991)
Show that when the density of the region is constant, the first moment about the -axis is
Short Answer
The first moment of the mass in about the axis is
Chapter 13: Q.14 (page 991)
Show that when the density of the region is constant, the first moment about the -axis is
The first moment of the mass in about the axis is
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Get started for freeDescribe the three-dimensional region expressed in each iterated integral in Exercises 35–44.
Evaluate each of the integrals in exercise 33-36 as iterated integrals and then compare your answers with those you found in exercise 29-32
Use Definition to evaluate the double integrals in Exercises .
where
Explain how to construct a Riemann sum for a function of three variables over a rectangular solid.
In 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.
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