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a) Suppose that F(x, y, z) = (x² + y)i + z²j+(e* -z)k i) Find the divergence of F(x, y, z). Hence, by using the Divergence Theorem, evaluate fF.ds where is the surface of the rectangular solid bounded by the coordinate planes and the planes x = 3, y = 1 and z = 2.

a) Suppose that F(x, y, z) = (x² + y)i + z²j+(e* -z)k i) Find the divergence of F(x, y, z). Hence, by using the Divergence Theorem, evaluate fF.ds where is the surface of the rectangular solid bounded by the coordinate planes and the planes x = 3, y = 1 and z = 2.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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a) Suppose that F(x, y, z) = (x² + y)i + z²j+(e* -z)k i) Find the divergence of F(x, y, z). Hence, by using the Divergence Theorem, evaluate fF-fids where is the surface of the rectangular solid bounded by the coordinate planes and the planes x = 3, y = 1 and z = 2. b) Let R be the region between circles x² + y² = 36 and x² + y² =1. Sketch the region and evaluate the line integral [2xydy + (x²+2x)dy using the Green's Theorem c) Use the Stoke's Theorem to evaluate [F. dr where F(x, y, z) = -y² + zj+ xk and C be the positive oriented triangle lying on the plane 2x +2y+z= 6 bounded by the coordinate planes.
Transcribed Image Text:a) Suppose that F(x, y, z) = (x² + y)i + z²j+(e* -z)k i) Find the divergence of F(x, y, z). Hence, by using the Divergence Theorem, evaluate fF-fids where is the surface of the rectangular solid bounded by the coordinate planes and the planes x = 3, y = 1 and z = 2. b) Let R be the region between circles x² + y² = 36 and x² + y² =1. Sketch the region and evaluate the line integral [2xydy + (x²+2x)dy using the Green's Theorem c) Use the Stoke's Theorem to evaluate [F. dr where F(x, y, z) = -y² + zj+ xk and C be the positive oriented triangle lying on the plane 2x +2y+z= 6 bounded by the coordinate planes.
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Solve b) and c)

a) Suppose that F(x, y, z) = (x² + y)i + z²j+(e* -z)k i) Find the divergence of F(x, y, z). Hence, by using the Divergence Theorem, evaluate fF-fids where is the surface of the rectangular solid bounded by the coordinate planes and the planes x = 3, y = 1 and z = 2. b) Let R be the region between circles x² + y² = 36 and x² + y² =1. Sketch the region and evaluate the line integral [2xydy + (x²+2x)dy using the Green's Theorem c) Use the Stoke's Theorem to evaluate [F. dr where F(x, y, z) = -y² + zj+ xk and C be the positive oriented triangle lying on the plane 2x +2y+z= 6 bounded by the coordinate planes.
Transcribed Image Text:a) Suppose that F(x, y, z) = (x² + y)i + z²j+(e* -z)k i) Find the divergence of F(x, y, z). Hence, by using the Divergence Theorem, evaluate fF-fids where is the surface of the rectangular solid bounded by the coordinate planes and the planes x = 3, y = 1 and z = 2. b) Let R be the region between circles x² + y² = 36 and x² + y² =1. Sketch the region and evaluate the line integral [2xydy + (x²+2x)dy using the Green's Theorem c) Use the Stoke's Theorem to evaluate [F. dr where F(x, y, z) = -y² + zj+ xk and C be the positive oriented triangle lying on the plane 2x +2y+z= 6 bounded by the coordinate planes.
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