Chapter 13: Q. 32 (page 1004)
Use definition to evaluate the double integral
Short Answer
The value of the integral is 126
Chapter 13: Q. 32 (page 1004)
Use definition to evaluate the double integral
The value of the integral is 126
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Get started for freeUse the results of Exercises 59 and 60 to find the centers of masses of the laminæ in Exercises 61–67.
In the following lamina, all angles are right angles and the density is constant:
Use the lamina from Exercise 64, but assume that the density is proportional to the distance from the x-axis.
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 double integral in the exercise 37-54 as iterated integrals
Evaluate the sums in Exercises .
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