Chapter 13: Q 46. (page 1039)
If the density at each point in is proportional to the point’s distance from the -axis, find the mass of .
Short Answer
The mass of region is
Chapter 13: Q 46. (page 1039)
If the density at each point in is proportional to the point’s distance from the -axis, find the mass of .
The mass of region is
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Get started for freeIdentify the quantities determined by the integral expressions in Exercises 19–24. If x, y, and z are all measured in centimeters and ρ(x, y,z) is a density function in grams per cubic centimeter on the three-dimensional region , give the units of the expression.
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.
In the following lamina, all angles are right angles and the density is constant:
Let f(x, y, z) and g(x, y, z) be integrable functions on the rectangular solid . . Use the definition of the triple integral to prove that :
Describe the three-dimensional region expressed in each iterated integral in Exercises 35–44.
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