Chapter 13: Q 33. (page 1039)
Let be triangular region with vertices
If the density at each point in is proportional to the point’s distance from the -axis, find the center of mass of .
Short Answer
The center of mass is
Chapter 13: Q 33. (page 1039)
Let be triangular region with vertices
If the density at each point in is proportional to the point’s distance from the -axis, find the center of mass of .
The center of mass is
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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}.
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.
Use the lamina from Exercise 64, but assume that the density is proportional to the distance from the x-axis.
Evaluate the triple integrals over the specified rectangular solid region.
Explain why using an iterated integral to evaluate a double integral is often easier than using the definition of the double integral to evaluate the integral.
Evaluate each of the double integral in the exercise 37-54 as iterated integrals
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