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 freeIn 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.
In Exercises 61–64, let R be the rectangular solid defined by
Assume that the density of R is uniform throughout, and find the moment of inertia about the x-axis and the radius of gyration about the x-axis.
Find the masses of the solids described in Exercises 53–56.
The solid bounded above by the paraboloid with equation and bounded below by the rectangle in the xy-plane if the density at each point is proportional to the square of the distance of the point from the origin.
Evaluate the triple integrals over the specified rectangular solid region.
Explain how to construct a Riemann sum for a function of three variables over a rectangular solid.
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