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(a). Evaluate ff F-n dS, where F(x, y, z) = (2x − z, x²y, −xz²), and S is the surface of the cube bounded by x=0, x= 1, y = 0, y = 1, z = 0, and z = 1. (b). Evaluate SSS div F dV where E is the solid region of the same cube.

(a). Evaluate ff F-n dS, where F(x, y, z) = (2x − z, x²y, −xz²), and S is the surface of the cube bounded by x=0, x= 1, y = 0, y = 1, z = 0, and z = 1. (b). Evaluate SSS div F dV where E is the solid region of the same cube.

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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Verify the Gauss Divergence Theorem for the following vector field (image attached)

(a). Evaluate f F n dS, where F(x, y, z) = (2x — z, x²y, -xz²), and S is the surface of the cube bounded by x = 0, x= 1, y = 0, y = 1, z = 0, and z = 1. (b). Evaluate fff div F dV where E is the solid region of the same cube.
Transcribed Image Text:(a). Evaluate f F n dS, where F(x, y, z) = (2x — z, x²y, -xz²), and S is the surface of the cube bounded by x = 0, x= 1, y = 0, y = 1, z = 0, and z = 1. (b). Evaluate fff div F dV where E is the solid region of the same cube.
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