Chapter 13: Q. 22 (page 1038)
Complete Example 2 by showing that
Short Answer
The mass of semicircular lamina is
Chapter 13: Q. 22 (page 1038)
Complete Example 2 by showing that
The mass of semicircular lamina is
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Get started for freeIn Exercises 45–52, rewrite the indicated integral with the specified order of integration.
Exercise 42 with the order dy dx dz.
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
Use Definition to evaluate the double integrals in Exercises .
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where
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.
In Exercises, let
If the density at each point in S is proportional to the point’s distance from the origin, find the center of mass of S.
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