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1. Let E be the surface in R³ given by z = e-¤²-y" where x² + y? < 4, oriented with the upward normal. Let F be the vector field given by F(x, y, z) = (y, –x, x²). Compute the flux F.dA.

1. Let E be the surface in R³ given by z = e-¤²-y" where x² + y? < 4, oriented with the upward normal. Let F be the vector field given by F(x, y, z) = (y, –x, x²). Compute the flux F.dA.

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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1. Let E be the surface in R³ given by z = e-¤²-y" where x² + y² < 4, oriented with the upward normal. Let F be the vector field given by F(x, y, z) = (y, –x, x²). Compute the flux F. dA. Σ 2. Let y be the curve in R3 given by t+ (t, 2 cos t, 2 sin t) for 0 <t < 47. Compute ds 3. Let R be the solid cone in R³ given by z > Vx² + y² and z < 1. Let E be the boundary of R, oriented outwards. Let F be the vector field given by F(x, y, z) = (x³, y³, z³). Compute F. dA.
Transcribed Image Text:1. Let E be the surface in R³ given by z = e-¤²-y" where x² + y² < 4, oriented with the upward normal. Let F be the vector field given by F(x, y, z) = (y, –x, x²). Compute the flux F. dA. Σ 2. Let y be the curve in R3 given by t+ (t, 2 cos t, 2 sin t) for 0 <t < 47. Compute ds 3. Let R be the solid cone in R³ given by z > Vx² + y² and z < 1. Let E be the boundary of R, oriented outwards. Let F be the vector field given by F(x, y, z) = (x³, y³, z³). Compute F. dA.
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