Chapter 13: Q. 37 (page 1055)
Describe the three-dimensional region expressed in each iterated integral in Exercises 35–44.
Short Answer
The three-dimensional region is,
Chapter 13: Q. 37 (page 1055)
Describe the three-dimensional region expressed in each iterated integral in Exercises 35–44.
The three-dimensional 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.
Explain how the Fundamental Theorem of Calculus is used in evaluating the iterated integral .
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 ofR is uniform throughout.
(a) Without using calculus, explain why the center of mass is (2, 3/2, 1).
(b) Verify that the center of mass is (2, 3/2, 1), using the appropriate integral expressions.
Evaluate Each of the integrals in exercises 33-36 as an iterated integral and then compare your answer with thoise you found in exercise 29-32
Evaluate each of the double integrals in Exercisesas iterated integrals.
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