Chapter 13: Q. 64 (page 1040)
In the following lamina, all angles are right angles and the density is constant:
Short Answer
The Center of mass of lamina is
Chapter 13: Q. 64 (page 1040)
In the following lamina, all angles are right angles and the density is constant:
The Center of mass of lamina is
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Get started for freeExplain 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.
What is the difference between a triple integral and an iterated triple 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 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.
Use Definition to evaluate the double integrals in Exercises .
where
Evaluate each of the double integrals in Exercises 37–54 as iterated integrals.
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