STOKES' THEOREM o may be parameterized by r(r, y) = (1, y, f(x, y)) = curl F
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![STOKES' THEOREM
o may be parameterized by r(2, y) = (z, y, f(x, y)) =
curl F
(curl F) - nds
%3D
dydz
54/(sqrt140)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1f45e406-9121-47ca-afa3-0389a7bb5e53%2F6ebe38b0-9194-4193-809e-2aef88ac551d%2F0qf1nmt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:STOKES' THEOREM
o may be parameterized by r(2, y) = (z, y, f(x, y)) =
curl F
(curl F) - nds
%3D
dydz
54/(sqrt140)
![Let o be the surface 10r + 2y + 6z = 8 in the first octant, oriented upwards. Let C be the oriented boundary of a. Compute the
work done in moving a unit mass particle around the boundary of o through the vector field
F = (4x – 3y)i + (3y – 2)j + (z– 4x)k using line integrals, and using Stokes' Theorem.
Assume mass is measured in kg, length in meters, and force in Newtons (1 nt = 1kg-m).
LINE INTEGRALS
Parameterize the boundary of o positively using the standard form, tv+P with 0 <t< 1, starting with the segment in the xy
plane.
C (the edge in the xy plane) is parameterized by <4/5-4/5t,41,0>
C2 (the edge folowing C1) is parameterized by <0,4-41,4/3t>
C3 (the last edge) is parameterized by <4/5t,0,4/3-4/3t>
F dr= 688/25
C1
dr =
-136/9
F-dr =
dr=
STOKES' THEOREM](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1f45e406-9121-47ca-afa3-0389a7bb5e53%2F6ebe38b0-9194-4193-809e-2aef88ac551d%2F35zdu6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let o be the surface 10r + 2y + 6z = 8 in the first octant, oriented upwards. Let C be the oriented boundary of a. Compute the
work done in moving a unit mass particle around the boundary of o through the vector field
F = (4x – 3y)i + (3y – 2)j + (z– 4x)k using line integrals, and using Stokes' Theorem.
Assume mass is measured in kg, length in meters, and force in Newtons (1 nt = 1kg-m).
LINE INTEGRALS
Parameterize the boundary of o positively using the standard form, tv+P with 0 <t< 1, starting with the segment in the xy
plane.
C (the edge in the xy plane) is parameterized by <4/5-4/5t,41,0>
C2 (the edge folowing C1) is parameterized by <0,4-41,4/3t>
C3 (the last edge) is parameterized by <4/5t,0,4/3-4/3t>
F dr= 688/25
C1
dr =
-136/9
F-dr =
dr=
STOKES' THEOREM
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)