Chapter 13: Q. 62 (page 1005)
Find the volume between the graph of the given function and the xy-plane over the specified rectangle in the xy-plane
Short Answer
Volume of the integral is
Chapter 13: Q. 62 (page 1005)
Find the volume between the graph of the given function and the xy-plane over the specified rectangle in the xy-plane
Volume of the integral is
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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 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 the triple integrals over the specified rectangular solid region.
Find the volume between the graph of the given function and the xy-plane over the specified rectangle in the xy-plane
Evaluate Each of the integrals in exercises 33-36 as an iterated integral and then compare your answer with thoise you found in exercise 29-32
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