Chapter 13: Q. 44 (page 1027)
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. 44 (page 1027)
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 an integrable function on the rectangular solid , and let Use the definition of the triple integral to prove that:
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.
Evaluate Each of the integrals in exercises 33-36 as an iterated integral and then compare your answer with thoise you found in exercise 29-32
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.
How many summands are in ?
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