Chapter 13: Q. 64 (page 1040)
In the following lamina, all angles are right angles and the density is constant:
Short Answer
The Center of mass of lamina is
Chapter 13: Q. 64 (page 1040)
In the following lamina, all angles are right angles and the density is constant:
The Center of mass of lamina is
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Get started for freeDescribe the three-dimensional region expressed in each iterated integral in Exercises 35–44.
Explain how the Fundamental Theorem of Calculus is used in 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.
(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.
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.
Explain why using an iterated integral to evaluate a double integral is often easier than using the definition of the double integral to evaluate the integral.
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