Chapter 13: Q 15. (page 1066)
The volume increment when you use spherical coordinates to evaluate a triple integral. Why is this the standard order of integration for spherical
coordinates?
Chapter 13: Q 15. (page 1066)
The volume increment when you use spherical coordinates to evaluate a triple integral. Why is this the standard order of integration for spherical
coordinates?
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Get started for freeEvaluate the sums in Exercises .
Explain why it would be difficult to evaluate the double integrals in Exercises 18 and 19 as iterated integrals.
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.
Evaluate each of the integrals in exercise 33-36 as iterated integrals and then compare your answers with those you found in exercise 29-32
Evaluate each of the double integral in the exercise 37-54 as iterated integrals
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