Chapter 13: Q. 18 (page 1055)
Complete Example by evaluating the iterated integral
Short Answer
The value of the iterated integral is,.
Chapter 13: Q. 18 (page 1055)
Complete Example by evaluating the iterated integral
The value of the iterated integral is,.
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Get started for freeState Fubini's theorem.
Use the results of Exercises 59 and 60 to find the centers of masses of the laminæ in Exercises 61–67.
In the following lamina, all angles are right angles and the density is constant:
Explain 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 .
In Exercises 57–60, let R be the rectangular solid defined by
R = {(x, y, z) | 0 ≤ x ≤ 4, 0 ≤ y ≤ 3, 0 ≤ z ≤ 2}.
Assume that the density of R is uniform throughout, and find the moment of inertia about the x-axis and the radius of gyration about the x-axis.
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
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