Let S₁ be the part of the paraboloid z = x² + y² − 1 that lies below the plane z = 3 and S₁ has downward orientation. Let F(x, y, z) = zi+xj + (x +z)k. (a). Verify that Stokes' Theorem is true for F and S₁. (b). Let S₂ be the disk x² + y² ≤ 4 on plane z = 3 and S = S₁ + S₂. E is the solid bounded by S. Use the Divergence Theorem to calculate the flux of F across S.
Let S₁ be the part of the paraboloid z = x² + y² − 1 that lies below the plane z = 3 and S₁ has downward orientation. Let F(x, y, z) = zi+xj + (x +z)k. (a). Verify that Stokes' Theorem is true for F and S₁. (b). Let S₂ be the disk x² + y² ≤ 4 on plane z = 3 and S = S₁ + S₂. E is the solid bounded by S. Use the Divergence Theorem to calculate the flux of F across S.
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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Let S₁ be the part of the paraboloid z = x² + y² − 1 that lies below the plane z = 3 and S₁ has downward orientation. Let F(x, y, z) = zi+xj + (x +z)k.
(a). Verify that Stokes' Theorem is true for F and S₁.
(b). Let S₂ be the disk x² + y² ≤ 4 on plane z = 3 and S = S₁ + S₂. E is the solid bounded by S. Use the Divergence Theorem to calculate the flux of F across S.
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