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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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.
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.
Explain why using an iterated integral to evaluate a double integral is often easier than using the definition of the double integral to evaluate the integral.
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