Chapter 13: Q. 15 (page 1038)
Show that when the density of the region is proportional to the distance from the -axis, the mass of is given by
Short Answer
the mass of is given by
Chapter 13: Q. 15 (page 1038)
Show that when the density of the region is proportional to the distance from the -axis, the mass of is given by
the mass of is given by
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Get started for freeIn Exercises 45–52, rewrite the indicated integral with the specified order of integration.
Exercise 42 with the order dy dx dz.
In the following lamina, all angles are right angles and the density is constant:
Evaluate the sums in Exercises .
Evaluate the iterated integral :
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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