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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Get started for freeIn Exercises 45–52, rewrite the indicated integral with the specified order of integration.
Exercise 41 with the order dy dx dz.
Evaluate each of the double integral in the exercise 37-54 as iterated integrals
Find the volume between the graph of the given function and the xy-plane over the specified rectangle in the xy-plane
In Exercises 61–64, let R be the rectangular solid defined by
Assume that the density of R is uniform throughout.
(a) Without using calculus, explain why the center of
mass is
(b) Verify that is the center of mass by using the appropriate integral expressions.
Use the results of Exercises 59 and 60 to find the centers of masses of the laminæ in Exercises 61–67.
Use the lamina from Exercise 61, but assume that the density is proportional to the distance from the x-axis.
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