Chapter 5: Q33P (page 257)
Verify that (3.10) gives the same result as (3.8).
Short Answer
The given equation is verified.
Chapter 5: Q33P (page 257)
Verify that (3.10) gives the same result as (3.8).
The given equation is verified.
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Get started for freeFind the mass of the solid in Problem 5 if the density is . Check your work by doing the problem in both spherical and cylindrical coordinates.
Hints: Sketch a right triangle with acute angles u and v and label the sides so that sinu=Kr. Also, note that; then if u is an indefinite integral, so is -v since they differ by a constant of integration.
Under the surface z = 1 /(y+2) , and over the area bounded by and y=x .
A lamina covering the quarter disk has (area) density . Find the mass of the lamina.
Use Problems 12 and 13 to find the centroids of a semi-circular area and of a semi-circular arc. Hint: Assume the formulas , for a sphere.
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