Calculate the circulation, SoF. dr. in two ways, directly and using Stokes' Theorem. The vector field F = 6yi - 6x3 and C is the boundary of S, the part of the surface z = 9x² - y² above the xy-plane, oriented upward. Note that is a circle in the cy-plane. Find a r(t) that parameterizes this curve. F(t) = 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 SoF.drdt, where a and b are the endpoints you gave above. Evaluate your integral to find the circulation: SF. d= Using Stokes' Theorem, we equate f. dr = ff, curl F. dÃ. Find curl = Noting that the surface is given by z=9x² - y², use cylindrical coordinates to give a parametrization of the surface (write theta for 0 ): r(r, 0) with 0
Calculate the circulation, SoF. dr. in two ways, directly and using Stokes' Theorem. The vector field F = 6yi - 6x3 and C is the boundary of S, the part of the surface z = 9x² - y² above the xy-plane, oriented upward. Note that is a circle in the cy-plane. Find a r(t) that parameterizes this curve. F(t) = 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 SoF.drdt, where a and b are the endpoints you gave above. Evaluate your integral to find the circulation: SF. d= Using Stokes' Theorem, we equate f. dr = ff, curl F. dÃ. Find curl = Noting that the surface is given by z=9x² - y², use cylindrical coordinates to give a parametrization of the surface (write theta for 0 ): r(r, 0) with 0
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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![Calculate the circulation, SF. dr. in two ways, directly and using Stokes' Theorem. The vector field F – 6yi – 6x3 and C is the boundary of S, the part of the surface z = 9 - 2² - y² above the xy-plane, oriented
upward.
Note that C is a circle in the cy-plane. Find a 7(t) that parameterizes this curve.
F(t) =
+50
with
(Note that answers must be provided for all three of these answer blanks to
With this parameterization, the circulation integral is
ScF • dr = So
Evaluate your integral to find the circulation: SF. dr =
dt, where a and b are the endpoints you gave above.
Using Stokes' Theorem, we equate f. d=ff, curl F. dÃ.
Find curl F =
Noting that the surface is given by z = 9x² - y², use cylindrical coordinates to give a parametrization of the surface (write theta for 0 ):
r(r, 0)
with 0≤r≤3 and 0 ≤0 ≤ 2π
With R giving the appropriate region in polar coordinates, this gives
ff curl F· dÃ=ffR [0] dr de.
able to determine correctness of the parameterization.)
Evaluate this integral to find the circulation:
SoFd=ffs curl F. dÃ](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6544980f-78eb-42c1-bdf7-a346dd2568f1%2F0b58727c-744c-41d9-b378-a09529a266fc%2Fycs2xft_processed.png&w=3840&q=75)
Transcribed Image Text:Calculate the circulation, SF. dr. in two ways, directly and using Stokes' Theorem. The vector field F – 6yi – 6x3 and C is the boundary of S, the part of the surface z = 9 - 2² - y² above the xy-plane, oriented
upward.
Note that C is a circle in the cy-plane. Find a 7(t) that parameterizes this curve.
F(t) =
+50
with
(Note that answers must be provided for all three of these answer blanks to
With this parameterization, the circulation integral is
ScF • dr = So
Evaluate your integral to find the circulation: SF. dr =
dt, where a and b are the endpoints you gave above.
Using Stokes' Theorem, we equate f. d=ff, curl F. dÃ.
Find curl F =
Noting that the surface is given by z = 9x² - y², use cylindrical coordinates to give a parametrization of the surface (write theta for 0 ):
r(r, 0)
with 0≤r≤3 and 0 ≤0 ≤ 2π
With R giving the appropriate region in polar coordinates, this gives
ff curl F· dÃ=ffR [0] dr de.
able to determine correctness of the parameterization.)
Evaluate this integral to find the circulation:
SoFd=ffs curl F. dÃ
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