Chapter 13: Q.46 (page 991)
Each of the integrals or integral expressions in Exercises 39–46 represents the volume of a solid in . Use polar coordinates to describe the solid, and evaluate the expressions
Short Answer
The value of integral is
Chapter 13: Q.46 (page 991)
Each of the integrals or integral expressions in Exercises 39–46 represents the volume of a solid in . Use polar coordinates to describe the solid, and evaluate the expressions
The value of integral is
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Get started for freeLet be a lamina in the xy-plane. Suppose is composed of two non-overlapping lamin and , as follows:
Show that if the masses and centers of masses of and are and and respectively, then the center of mass of is where
Use 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.
Evaluate the sums in Exercises 23–28.
Evaluate each of the double integrals in Exercises 37–54 as iterated integrals.
Describe the three-dimensional region expressed in each iterated integral in Exercises 35–44.
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