Chapter 13: Q 73. (page 1006)
Let be real numbers and be rectangle defined by
in plane. If is continuous in interval and is continuous on
Use Fubini's theorem to prove that
Short Answer
It can be proved using definition of Fubini's theorem
.
Chapter 13: Q 73. (page 1006)
Let be real numbers and be rectangle defined by
in plane. If is continuous in interval and is continuous on
Use Fubini's theorem to prove that
It can be proved using definition of Fubini's theorem
.
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Get started for freeEvaluate each of the integrals in exercise 33-36 as iterated integrals and then compare your answers with those you found in exercise 29-32
How many summands are in ?
In Exercises 61–64, let R be the rectangular solid defined by
Assume that the density of R is uniform throughout.
(a) Without using calculus, explain why the center of
mass is
(b) Verify that is the center of mass by using the appropriate integral expressions.
Evaluate each of the double integrals in Exercisesas iterated integrals.
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wherelocalid="1650380496793"
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}.
Assuming that the density at each point in R is proportional to the distance of the point from the xy-plane, find the moment of inertia about the x-axis and the radius of gyration about the x-axis.
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