Chapter 13: Q. 15 (page 1038)
Show that when the density of the region is proportional to the distance from the -axis, the mass of is given by
Short Answer
the mass of is given by
Chapter 13: Q. 15 (page 1038)
Show that when the density of the region is proportional to the distance from the -axis, the mass of is given by
the mass of is given by
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If the density at each point in S is proportional to the point’s distance from the origin, find the moments of inertia about the x-axis, the y-axis, and the origin. Use these answers to find the radii of gyration of S about the x-axis, the y-axis, and the origin.
Describe the three-dimensional region expressed in each iterated integral in Exercises 35–44.
Let be an integrable function on the rectangular solid , and let Use the definition of the triple integral to prove that:
Discuss the similarities and differences between the definition of the double integral found in Section and the definition of the triple integral found in this section.
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