Chapter 13: Q. 43 (page 1027)
Each of the integrals or integral expressions in Exercises 39-46 represents the volume of a solid in . Use polar coordinates to describe the solid, and evaluate the expressions.
Short Answer
The value of integral is
Chapter 13: Q. 43 (page 1027)
Each of the integrals or integral expressions in Exercises 39-46 represents the volume of a solid in . Use polar coordinates to describe the solid, and evaluate the expressions.
The value of integral is
All the tools & learning materials you need for study success - in one app.
Get started for freeIn Exercises, let
If the density at each point in S is proportional to the point’s distance from the origin, find the center of mass of S.
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}.
Assuming that the density at each point in R is proportional to the distance of the point from the xy-plane, find the moment of inertia about the x-axis and the radius of gyration about the x-axis.
Identify 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.
Describe the three-dimensional region expressed in each iterated integral in Exercises 35–44.
Evaluate the sums in Exercises .
What do you think about this solution?
We value your feedback to improve our textbook solutions.