Chapter 13: Q.25 (page 1082)
Evaluating triple integrals: Each of the triple integrals that follow represents the volume of a solid. Sketch the solid and evaluate the integral.
Short Answer
The value of the triple integral is 30.
Chapter 13: Q.25 (page 1082)
Evaluating triple integrals: Each of the triple integrals that follow represents the volume of a solid. Sketch the solid and evaluate the integral.
The value of the triple integral is 30.
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Get started for freeExplain how to construct a midpoint Riemann sum for a function of three variables over a rectangular solid for which each is the midpoint of the subsolid role="math" localid="1650346869585" . Refer either to your answer to Exercise or to Definition .
Evaluate each of the double integrals in Exercisesas iterated integrals.
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wherelocalid="1650380496793"
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.
In Exercises 45–52, rewrite the indicated integral with the specified order of integration.
Exercise 41 with the order dy dx dz.
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