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Calculate the circulation, feF. dr, in two ways, directly and using Stokes' Theorem. The vector field F = 8yi - 8xj and C is the boundary of S, the part of the surface z = 4 - x² above the ay-plane, oriented upward. Note that C is a circle in the xy-plane. Find a r(t) that parameterizes this curve. F(t) = 9. with st≤ (Note that answers must be provided for all three of these answer blanks to be able to determine correctness of the parameterization.) With this parameterization, the circulation integral is ScF.dr = Sa Evaluate your integral to find the circulation: fc F. dr = dt, where a and b are the endpoints you gave above. Using Stokes' Theorem, we equate foF dr = f curl F. dÃ. Find curl F = Noting that the surface is given by z=4 - x² - y², find A = dy dr. With R giving the region in the zy-plane enclosed by the surface, this gives Is curl F. dà = SR dy dr. Evaluate this integral to find the circulation: ScF. dr = fg curl F. dà =

Calculate the circulation, feF. dr, in two ways, directly and using Stokes' Theorem. The vector field F = 8yi - 8xj and C is the boundary of S, the part of the surface z = 4 - x² above the ay-plane, oriented upward. Note that C is a circle in the xy-plane. Find a r(t) that parameterizes this curve. F(t) = 9. with st≤ (Note that answers must be provided for all three of these answer blanks to be able to determine correctness of the parameterization.) With this parameterization, the circulation integral is ScF.dr = Sa Evaluate your integral to find the circulation: fc F. dr = dt, where a and b are the endpoints you gave above. Using Stokes' Theorem, we equate foF dr = f curl F. dÃ. Find curl F = Noting that the surface is given by z=4 - x² - y², find A = dy dr. With R giving the region in the zy-plane enclosed by the surface, this gives Is curl F. dà = SR dy dr. Evaluate this integral to find the circulation: ScF. dr = fg curl F. dà =

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
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how do i solve the attached calculus problem?

Calculate the circulation, foF. dr, in two ways, directly and using Stokes' Theorem. The vector field F = 8yi - 8xj and C is the boundary of S, the part of the surface z = 4 — x² - y² above the xy-plane, oriented upward. Note that C is a circle in the xy-plane. Find a r(t) that parameterizes this curve. r(t) = with I <t< (Note that answers must be provided for all three of these answer blanks to be able to determine correctness of the parameterization.) With this parameterization, the circulation integral is fe Evaluate your integral to find the circulation: fc F. dr = ScF. dr = dt, where a and b are the endpoints you gave above. Using Stokes' Theorem, we equate SF. dr = f curl F · dÃ. Find curl F - Noting that the surface is given by 2=4x² - y², find dà = dy dx. With R giving the region in the xy-plane enclosed by the surface, this gives Ss curl F. dà = SR dy dx. Evaluate this integral to find the circulation: ScF. dr = f curl F. dÃ
Transcribed Image Text:Calculate the circulation, foF. dr, in two ways, directly and using Stokes' Theorem. The vector field F = 8yi - 8xj and C is the boundary of S, the part of the surface z = 4 — x² - y² above the xy-plane, oriented upward. Note that C is a circle in the xy-plane. Find a r(t) that parameterizes this curve. r(t) = with I <t< (Note that answers must be provided for all three of these answer blanks to be able to determine correctness of the parameterization.) With this parameterization, the circulation integral is fe Evaluate your integral to find the circulation: fc F. dr = ScF. dr = dt, where a and b are the endpoints you gave above. Using Stokes' Theorem, we equate SF. dr = f curl F · dÃ. Find curl F - Noting that the surface is given by 2=4x² - y², find dà = dy dx. With R giving the region in the xy-plane enclosed by the surface, this gives Ss curl F. dà = SR dy dx. Evaluate this integral to find the circulation: ScF. dr = f curl F. dÃ
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