Chapter 13: Q.29 (page 991)
If the density at each point in is proportional to the point's distance from the -axis, find the center of mass of .
Short Answer
Area of the region bounded by the spiral and the -axis is
Chapter 13: Q.29 (page 991)
If the density at each point in is proportional to the point's distance from the -axis, find the center of mass of .
Area of the region bounded by the spiral and the -axis is
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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}.
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.
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.
Evaluate each of the double integrals in Exercises 37–54 as iterated integrals.
Evaluate the triple integrals over the specified rectangular solid region.
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}.
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.
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