Chapter 13: Q 43. (page 1039)
Let be rectangle with coordinates
If the density at each point in is proportional to the square of the point’s distance from the -axis, find the center of mass of .
Short Answer
The center of mass is.
Chapter 13: Q 43. (page 1039)
Let be rectangle with coordinates
If the density at each point in is proportional to the square of the point’s distance from the -axis, find the center of mass of .
The center of mass 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 center of mass of S.
Evaluate each of the double integrals in Exercises 37–54 as iterated integrals.
Evaluate the iterated integral :
Evaluate each of the double integral in the exercise 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.
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