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 freeIn Exercises 45–52, rewrite the indicated integral with the specified order of integration.
Exercise 42 with the order dy dx dz.
Evaluate each of the double integrals in Exercises 37–54 as iterated integrals.
Find 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 iterated integral :
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