Chapter 13: Q. 42 (page 1079)
Evaluate the double integrals in Exercises 39–48. Use suitable transformations as necessary.
, where R is the parallelogram from Exercise 41
Chapter 13: Q. 42 (page 1079)
Evaluate the double integrals in Exercises 39–48. Use suitable transformations as necessary.
, where R is the parallelogram from Exercise 41
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Get started for freeIdentify 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.
Evaluate the triple integrals over the specified rectangular solid region.
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 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.
Evaluate the iterated integral :
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
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