Chapter 13: Q 14. (page 1066)
The volume increment when you use cylindrical coordinates to evaluate a triple integral. Why is this the standard order of integration for cylindrical coordinates?
Short Answer
The volume increment is.
Chapter 13: Q 14. (page 1066)
The volume increment when you use cylindrical coordinates to evaluate a triple integral. Why is this the standard order of integration for cylindrical coordinates?
The volume increment is.
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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 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 of R is uniform throughout, and find the moment of inertia about the x-axis and the radius of gyration about the x-axis.
Evaluate each of the double integral in the exercise 37-54 as iterated integrals
Discuss the similarities and differences between the definition of the definite integral found in Chapter 4 and the definition of the double integral found in this section.
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