Chapter 13: Q. 18 (page 1055)
Complete Example by evaluating the iterated integral
Short Answer
The value of the iterated integral is,.
Chapter 13: Q. 18 (page 1055)
Complete Example by evaluating the iterated integral
The value of the iterated integral is,.
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Get started for freeUse Definition to evaluate the double integrals in Exercises .
where
Identify 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 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.
Describe the three-dimensional region expressed in each iterated integral in Exercises 35–44.
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.
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