Chapter 13: Q. 19 (page 1082)
Using polar coordinates to evaluate iterated integrals: Sketch the region determined by the limits of the given iterated integrals, and then evaluate the integrals.
Chapter 13: Q. 19 (page 1082)
Using polar coordinates to evaluate iterated integrals: Sketch the region determined by the limits of the given iterated integrals, and then evaluate the integrals.
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Get started for freeUse the results of Exercises 59 and 60 to find the centers of masses of the laminæ in Exercises 61–67.
Use the lamina from Exercise 61, but assume that the density is proportional to the distance from the x-axis.
Identify the quantities determined by the integral expressions in Exercises 19–24. If x, y, and z are all measured in centimeters and ρ(x, y,z) is a density function in grams per cubic centimeter on the three-dimensional region , give the units of the expression.
Discuss the similarities and differences between the definition of the double integral found in Section
In Exercises, let
If the density at each point in S is proportional to the point’s distance from the origin, find the moments of inertia about the x-axis, the y-axis, and the origin. Use these answers to find the radii of gyration of S about the x-axis, the y-axis, and the origin.
Evaluate each of the double integrals in Exercises 37–54 as iterated integrals.
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