Chapter 13: Q 38. (page 1039)
Let be rectangular region with vertices
Find the centroid of
Short Answer
The centroid is
Chapter 13: Q 38. (page 1039)
Let be rectangular region with vertices
Find the centroid of
The centroid is
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Get started for freeExplain how the Fundamental Theorem of Calculus is used in evaluating the iterated integral.
Evaluate each of the double integrals in Exercises 37–54 as iterated integrals.
Evaluate the sums in Exercises .
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.
Explain why it would be difficult to evaluate the double integrals in Exercises 18 and 19 as iterated integrals.
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