Chapter 13: Q. 19 (page 1038)
Show that when the density of the region is proportional to the distance from the -axis, the first moment about the -axis is
Short Answer
The moment of inertia about x-axis is
Chapter 13: Q. 19 (page 1038)
Show that when the density of the region is proportional to the distance from the -axis, the first moment about the -axis is
The moment of inertia about x-axis is
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Get started for freeEvaluate the sums in Exercises 23–28.
Evaluate the sums in Exercises
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 at each point in Ris proportional to the distance of the point from the xy-plane.
(a) Without using calculus, explain why the x- and y-coordinates of the center of mass are respectively.
(b) Use an appropriate integral expression to find the z-coordinate of the center of mass.
In the following lamina, all angles are right angles and the density is constant:
What is the difference between a triple integral and an iterated triple integral?
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