Chapter 13: Q. 24 (page 1082)
Using polar coordinates to evaluate iterated integrals: Evaluate the given iterated integrals by converting them to polar coordinates. Include a sketch of the region.
Chapter 13: Q. 24 (page 1082)
Using polar coordinates to evaluate iterated integrals: Evaluate the given iterated integrals by converting them to polar coordinates. Include a sketch of the region.
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Get started for freeIn Exercises 57–60, let R be the rectangular solid defined by
R = {(x, y, z) | 0 ≤ x ≤ 4, 0 ≤ y ≤ 3, 0 ≤ z ≤ 2}.
Assuming that the density at each point in R is proportional to the distance of the point from the xy-plane, find the moment of inertia about the x-axis and the radius of gyration about the x-axis.
Evaluate the sums in Exercises 23–28.
Describe the three-dimensional region expressed in each iterated integral in Exercises 35–44.
In 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.
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