Chapter 13: Q. 25 (page 1024)
Each of the integrals or integral expressions in Exercise represents the area of a region in the plane. Use polar coordinates to sketch the region and evaluate the expressions.
Short Answer
The integral's value is
Chapter 13: Q. 25 (page 1024)
Each of the integrals or integral expressions in Exercise represents the area of a region in the plane. Use polar coordinates to sketch the region and evaluate the expressions.
The integral's value is
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If the density at each point in S is proportional to the point’s distance from the origin, find the center of mass of S.
Earlier 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.
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 integrals in Exercises 37–54 as iterated integrals.
Use the results of Exercises 59 and 60 to find the centers of masses of the laminæ in Exercises 61–67.
In the following lamina, all angles are right angles and the density is constant:
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