Chapter 13: Q 56. (page 1039)
Let
If the density at each point in S is proportional to the point’s distance from the origin, find the mass of S.
Short Answer
Answer is where k is the constant of proportionality.
Chapter 13: Q 56. (page 1039)
Let
If the density at each point in S is proportional to the point’s distance from the origin, find the mass of S.
Answer is where k is the constant of proportionality.
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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}.
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.
Evaluate the triple integrals over the specified rectangular solid region.
Use Definition to evaluate the double integrals in Exercises .
where
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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