Chapter 13: Q. 65 (page 1028)
Use a double integral in polar coordinates to prove that the volume of a sphere with radius is.
Short Answer
The volume of a sphere is
Chapter 13: Q. 65 (page 1028)
Use a double integral in polar coordinates to prove that the volume of a sphere with radius is.
The volume of a sphere is
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Get started for freeFind the masses of the solids described in Exercises 53–56.
The solid bounded above by the plane with equation 2x + 3y − z = 2 and bounded below by the triangle with vertices (1, 0, 0), (4, 0, 0), and (0, 2, 0) if the density at each point is proportional to the distance of the point from the
xy-plane.
Evaluate the triple integrals over the specified rectangular solid region.
Evaluate the triple integrals over the specified rectangular solid region.
Use Definition to evaluate the double integrals in Exercises .
where
Let be a continuous function of three variables, let localid="1650352548375" be a set of points in the -plane, and let localid="1650354983053" be a set of points in -space. Find an iterated triple integral equal to the triple integral localid="1650353288865" . How would your answer change iflocalid="1650352747263" ?
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