Chapter 13: Q 19. (page 1066)
Show that the mass of is by evaluating the integral:
Short Answer
Use spherical coordinates while evaluating using triple integral.
Chapter 13: Q 19. (page 1066)
Show that the mass of is by evaluating the integral:
Use spherical coordinates while evaluating using triple integral.
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Get started for freeFind 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 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.
Describe the three-dimensional region expressed in each iterated integral in Exercises 35–44.
Discuss the similarities and differences between the definition of the double integral found in Section and the definition of the triple integral found in this section.
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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