Learning Materials
Features
Discover
Chapter 13: Q. 14 (page 1003)
Explain why using an iterated integral to evaluate a double integral is often easier than using the definition of the double integral to evaluate the integral.
Ans:
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
Evaluate the iterated integral :
Let be a lamina in the xy-plane. Suppose is composed of two non-overlapping lamin and , as follows:
Show that if the masses and centers of masses of and are and and respectively, then the center of mass of is where
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.
Let be a lamina in the xy-plane. Suppose is composed of n non-overlapping laminæ role="math" localid="1650321722341" Show that if the masses of these laminæ are and the centers of masses are then the center of mass of is where
In Exercises 61–64, let R be the rectangular solid defined by
Assume that the density of R is uniform throughout.
(a) Without using calculus, explain why the center of
mass is
(b) Verify that is the center of mass by using the appropriate integral expressions.
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Exams 
GCSE 
IGCSE 
AS 
A Level 
International A Level 
University Admissions Tests 
Flashcards 
Vaia AI 
Notes 
Study Plans 
Study Sets 
Find a job 
Find a degree 
Student Deals 
Magazine 
Mobile App