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 double integrals in Exercises 37–54 as iterated integrals.
Evaluate the iterated integral :
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.
Earlier in this section, we showed that we could use Fubini’s theorem to evaluate the integral and we showed that Now evaluate the double integral by evaluating the iterated integral.
Explain how the Fundamental Theorem of Calculus is used in evaluating the iterated integral.
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