Chapter 13: Q 52 (page 1005)
Evaluate each of the double integrals in Exercises as iterated integrals.
where.
Short Answer
The value of double integral is :-
where,
Chapter 13: Q 52 (page 1005)
Evaluate each of the double integrals in Exercises as iterated integrals.
where.
The value of double integral is :-
where,
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Get started for freeLet be a lamina in the xy-plane. Suppose is composed of two non-overlapping lamin and , as follows:
Show that if the masses and centers of masses of and are and and respectively, then the center of mass of is where
Evaluate the triple integrals over the specified rectangular solid region.
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.
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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