Chapter 13: Q. 44 (page 1004)
Evaluate each of the double integrals in Exercises 37–54 as iterated integrals.
Short Answer
The value is
Chapter 13: Q. 44 (page 1004)
Evaluate each of the double integrals in Exercises 37–54 as iterated integrals.
The value is
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Get started for freeEvaluate each of the double integral in the exercise 37-54 as iterated integrals
Use Definition to evaluate the double integrals in Exercises .
where
Find the masses of the solids described in Exercises 53–56.
The first-octant solid bounded by the coordinate planes and the plane 3x + 4y + 6z = 12 if the density at each point is proportional to the distance of the point from the xz-plane.
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 the sums in Exercises 23–28.
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