Chapter 13: Q. 37 (page 1015)
In Exercises 35–40, find the volume of the solid bounded above by the given function over the specified region.
Region:
Short Answer
Volume bounded by given function is.
Chapter 13: Q. 37 (page 1015)
In Exercises 35–40, find the volume of the solid bounded above by the given function over the specified region.
Region:
Volume bounded by given function is.
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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 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}.
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.
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