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integral to give the mass of the tetrahedron :

integral to give the mass of the tetrahedron :

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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the first image is the integral from question 3

8xyzdzdydx
Transcribed Image Text:8xyzdzdydx
4. There are several other ways we could have set up the integral to give the mass of the tetrahedron in the first octant bounded by the coordinate planes and the plane r+2y+3z = 6 with density d(r, y, z) = 8ryz. 5- 4+ 3. 2- (a) How many different iterated integrals could be set up that are equal to the integral in problem 3? (b) Set up an equivalent iterated integral, integrating first with respect to z, then x, then y. (c) Set up an equivalent iterated integral, integrating first with respect to y, then z, then r.
Transcribed Image Text:4. There are several other ways we could have set up the integral to give the mass of the tetrahedron in the first octant bounded by the coordinate planes and the plane r+2y+3z = 6 with density d(r, y, z) = 8ryz. 5- 4+ 3. 2- (a) How many different iterated integrals could be set up that are equal to the integral in problem 3? (b) Set up an equivalent iterated integral, integrating first with respect to z, then x, then y. (c) Set up an equivalent iterated integral, integrating first with respect to y, then z, then r.
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