Chapter 13: Q 14. (page 1014)
Explain why the double integral gives the area of the region . Illustrate your explanation with an example.
Short Answer
It is solved by solving type I integral.
Chapter 13: Q 14. (page 1014)
Explain why the double integral gives the area of the region . Illustrate your explanation with an example.
It is solved by solving type I integral.
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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.
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.
Describe the three-dimensional region expressed in each iterated integral in Exercises 35–44.
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
Evaluate the triple integrals over the specified rectangular solid region.
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