Chapter 13: Q.29 (page 991)
If the density at each point in is proportional to the point's distance from the -axis, find the center of mass of .
Short Answer
Area of the region bounded by the spiral and the -axis is
Chapter 13: Q.29 (page 991)
If the density at each point in is proportional to the point's distance from the -axis, find the center of mass of .
Area of the region bounded by the spiral and the -axis is
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Get started for freeEarlier in this section, we showed that we could use Fubini’s theorem to evaluate the integral and we showed that Now evaluate the double integral by evaluating the iterated integral.
Find the masses of the solids described in Exercises 53–56.
The first-octant solid bounded by the coordinate planes and the plane 3x + 4y + 6z = 12 if the density at each point is proportional to the distance of the point from the xz-plane.
Use Definition to evaluate the double integrals in Exercises .
where
In Exercises 61–64, let R be the rectangular solid defined by
Assume that the density of R is uniform throughout, and find the moment of inertia about the x-axis and the radius of gyration about the x-axis.
Evaluate each of the double integral in the exercise 37-54 as iterated integrals
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