Chapter 13: Q. 64 (page 1028)
Use a double integral to prove that the area of the circle with radius and equation is.
Short Answer
The area of the circle is
Chapter 13: Q. 64 (page 1028)
Use a double integral to prove that the area of the circle with radius and equation is.
The area of the circle is
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Get started for freeEvaluate the sums in Exercises .
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
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 .
Evaluate the iterated integral :
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 ofR is uniform throughout.
(a) Without using calculus, explain why the center of mass is (2, 3/2, 1).
(b) Verify that the center of mass is (2, 3/2, 1), using the appropriate integral expressions.
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