Chapter 13: Q. 25 (page 1004)
Evaluate the sums in Exercises .
Short Answer
The value of the summation is
Chapter 13: Q. 25 (page 1004)
Evaluate the sums in Exercises .
The value of the summation is
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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.
Evaluate each of the double integral in the exercise 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}.
Assume that the density ofR is uniform throughout.
(a) Without using calculus, explain why the center of mass is (2, 3/2, 1).
(b) Verify that the center of mass is (2, 3/2, 1), using the appropriate integral expressions.
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