Chapter 13: Q 65. (page 1067)
Find the specified quantities for the solids described below:
The center of mass of the region from Exercise , assuming that the density of the region is constant.
Short Answer
The center of mass is given by.
Chapter 13: Q 65. (page 1067)
Find the specified quantities for the solids described below:
The center of mass of the region from Exercise , assuming that the density of the region is constant.
The center of mass is given by.
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Get started for freeEvaluate Each of the integrals in exercises 33-36 as an iterated integral and then compare your answer with thoise you found in exercise 29-32
Evaluate each of the double integrals in Exercises 37–54 as iterated integrals.
Evaluate each of the double integrals in Exercises 37–54 as iterated integrals.
In Exercises 57–60, let R be the rectangular solid defined by
R = {(x, y, z) | 0 ≤ x ≤ 4, 0 ≤ y ≤ 3, 0 ≤ z ≤ 2}.
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.
Find the masses of the solids described in Exercises 53–56.
The solid bounded above by the plane with equation 2x + 3y − z = 2 and bounded below by the triangle with vertices (1, 0, 0), (4, 0, 0), and (0, 2, 0) if the density at each point is proportional to the distance of the point from the
xy-plane.
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