Use Stokes Theorem to evaluate F = (+2z)i + (2y-z)j + (x+y-z²)k and C is the triangle with vertices 3 =(√²+2 O SF (1,0,0), (0,1,0), (0,0,1) oriented counterclockwise when viewed from above. (Hint: the traingle has a plane equation z = 1-x-y) 2 O F.dr where 2
Use Stokes Theorem to evaluate F = (+2z)i + (2y-z)j + (x+y-z²)k and C is the triangle with vertices 3 =(√²+2 O SF (1,0,0), (0,1,0), (0,0,1) oriented counterclockwise when viewed from above. (Hint: the traingle has a plane equation z = 1-x-y) 2 O F.dr where 2
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
![**Use Stokes' Theorem to evaluate \(\oint_{C} \mathbf{F} \cdot d\mathbf{r} \) where**
\[
\mathbf{F} = \left(\frac{x^3}{3} + 2z\right)\mathbf{i} + (2y - z)\mathbf{j} + (x + y - z^2)\mathbf{k}
\]
and \( C \) is the triangle with vertices \( (1, 0, 0) \), \( (0, 1, 0) \), and \( (0, 0, 1) \) oriented counterclockwise when viewed from above.
(Hint: the triangle has a plane equation \( z = 1 - x - y \))
- ○ 2
- ○ 1
- ○ \(\frac{1}{2}\)
- ○ \(\frac{3}{2}\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2e521a1e-f4ee-4c02-af71-8dfc2cc184d3%2Fbe9598d5-2080-4856-8010-997472ff2eeb%2Fwfitya4_processed.png&w=3840&q=75)
Transcribed Image Text:**Use Stokes' Theorem to evaluate \(\oint_{C} \mathbf{F} \cdot d\mathbf{r} \) where**
\[
\mathbf{F} = \left(\frac{x^3}{3} + 2z\right)\mathbf{i} + (2y - z)\mathbf{j} + (x + y - z^2)\mathbf{k}
\]
and \( C \) is the triangle with vertices \( (1, 0, 0) \), \( (0, 1, 0) \), and \( (0, 0, 1) \) oriented counterclockwise when viewed from above.
(Hint: the triangle has a plane equation \( z = 1 - x - y \))
- ○ 2
- ○ 1
- ○ \(\frac{1}{2}\)
- ○ \(\frac{3}{2}\)
Expert Solution
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 2 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
