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Suppose that R is a 3-dimensional chunk of some substance, and that the density at each point x, y, z) within it is given by the function 8 (x, y, z). Explain what the triple integral 8(x,y, z) dV R Represents physically, and give an intuitive explanation of why this is so.

Suppose that R is a 3-dimensional chunk of some substance, and that the density at each point x, y, z) within it is given by the function 8 (x, y, z). Explain what the triple integral 8(x,y, z) dV R Represents physically, and give an intuitive explanation of why this is so.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Suppose that R is a 3-dimensional chunk of some substance, and that the density at each point (x, y, z) within it is given by the function 8 (x, y, z). Explain what the triple integral I| 8(x, y, z) dV R Represents physically, and give an intuitive explanation of why this is so.
Transcribed Image Text:Suppose that R is a 3-dimensional chunk of some substance, and that the density at each point (x, y, z) within it is given by the function 8 (x, y, z). Explain what the triple integral I| 8(x, y, z) dV R Represents physically, and give an intuitive explanation of why this is so.
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