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Chapter 13: Q. 36 (page 1004)
Evaluate each of the integrals in exercise 33-36 as iterated integrals and then compare your answers with those you found in exercise 29-32
The value of the integral is
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Evaluate each of the double integrals in Exercises 37鈥�54 as iterated integrals.
In Exercises 57鈥�60, let R be the rectangular solid defined by
R = {(x, y, z) | 0 鈮� x 鈮� 4, 0 鈮� y 鈮� 3, 0 鈮� z 鈮� 2}.
Assume that the density at each point in Ris proportional to the distance of the point from the xy-plane.
(a) Without using calculus, explain why the x- and y-coordinates of the center of mass are respectively.
(b) Use an appropriate integral expression to find the z-coordinate of the center of mass.
In Exercises 45鈥�52, rewrite the indicated integral with the specified order of integration.
Exercise 42 with the order dy dx dz.
What is the difference between a double integral and an iterated integral?
Find the masses of the solids described in Exercises 53鈥�56.
The solid bounded above by the paraboloid with equation and bounded below by the rectangle in the xy-plane if the density at each point is proportional to the square of the distance of the point from the origin.
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