Chapter 13: Q.26 (page 1082)
Evaluating triple integrals: Each of the triple integrals that follow represents the volume of a solid. Sketch the solid and evaluate the integral.
Short Answer
The obtained integral is 32.
Chapter 13: Q.26 (page 1082)
Evaluating triple integrals: Each of the triple integrals that follow represents the volume of a solid. Sketch the solid and evaluate the integral.
The obtained integral is 32.
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 moments of inertia about the x-axis, the y-axis, and the origin. Use these answers to find the radii of gyration of S about the x-axis, the y-axis, and the origin.
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
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.
Discuss the similarities and differences between the definition of the definite integral found in Chapter 4 and the definition of the double integral found in this section.
Evaluate the triple integrals over the specified rectangular solid region.
What do you think about this solution?
We value your feedback to improve our textbook solutions.