Chapter 13: Q. 65 (page 1028)
Use a double integral in polar coordinates to prove that the volume of a sphere with radius is.
Short Answer
The volume of a sphere is
Chapter 13: Q. 65 (page 1028)
Use a double integral in polar coordinates to prove that the volume of a sphere with radius is.
The volume of a sphere is
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Get started for freeIn Exercises, let
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.
Evaluate the sums in Exercises .
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
In Exercises 61–64, let R be the rectangular solid defined by
Assume that the density of R is uniform throughout, and find the moment of inertia about the x-axis and the radius of gyration about the x-axis.
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