Chapter 13: Q.27 (page 991)
Each of the integrals or integral expressions in Exercises 27 represents the area of a region in the plane. Use polar coordinates to sketch the region and evaluate the expressions.
Short Answer
The value of integral is
Chapter 13: Q.27 (page 991)
Each of the integrals or integral expressions in Exercises 27 represents the area of a region in the plane. Use polar coordinates to sketch the region and evaluate the expressions.
The value of integral is
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In Exercises 61–64, let R be the rectangular solid defined by
Assume that the density of R is uniform throughout.
(a) Without using calculus, explain why the center of
mass is
(b) Verify that is the center of mass by using the appropriate integral expressions.
Evaluate each of the double integral in the exercise 37-54 as iterated integrals
Discuss the similarities and differences between the definition of the definite integral found in Chapter 4 and the definition of the double integral found in this section.
State Fubini's theorem.
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