Chapter 13: Q. 25 (page 991)
If the density at each point in is proportional to the point's distance from the y-axis, find the mass of
Short Answer
The mass of the triangular lamina is
Chapter 13: Q. 25 (page 991)
If the density at each point in is proportional to the point's distance from the y-axis, find the mass of
The mass of the triangular lamina is
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Get started for freeIn 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.
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 at each point in Ris proportional to the distance of the point from the xy-plane.
(a) Without using calculus, explain why the x- and y-coordinates of the center of mass are respectively.
(b) Use an appropriate integral expression to find the z-coordinate of the center of mass.
Evaluate each of the double integral in the exercise 37-54 as iterated integrals
Let be a continuous function of three variables, let be a set of points in the -plane, and let be a set of points in 3-space. Find an iterated triple integral equal to the the triple integral. How would your answer change if?
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