Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
(a) Compute the flux of the field F = r i+yj-zk across the cylindrical surface a + z = 1, 0

(a) Compute the flux of the field F = r i+yj-zk across the cylindrical surface a + z = 1, 0

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Vectors In Two And Three Dimensions
Section9.FOM: Focus On Modeling: Vectors Fields
Problem 12P
See similar textbooks
icon
Related questions
Question
(a) Compute the flux of the field F = ai+yj-zk across the cylindrical surface a+z = 1, 0 <y53 with an outward pointing normal. (b) Given that the curl of F is Vx F = i+2 j+ 3 k. Find the work done by F along the oriented square path from (1, -1,3) to (2, -1,3) to (2,0, 3) to (1,0,3) and back to (1, –1,3). %3D | (c) Let M be the surface with the equation a+y* + z = 9 that is above the right triangular region with vertices (0, 0), (1,0) and (1, 2). (i) Write down the vector function r(r, y) and domain of the parameterization for surface M. (ii) For the vector field F ri+yj+ (2 + y) k, evaluate F. M (iii) For the scalar function g(x, y, z) = xz, set up but do not evaluate an iterated double integral that gives the surface integral of g over M.
Transcribed Image Text:(a) Compute the flux of the field F = ai+yj-zk across the cylindrical surface a+z = 1, 0 <y53 with an outward pointing normal. (b) Given that the curl of F is Vx F = i+2 j+ 3 k. Find the work done by F along the oriented square path from (1, -1,3) to (2, -1,3) to (2,0, 3) to (1,0,3) and back to (1, –1,3). %3D | (c) Let M be the surface with the equation a+y* + z = 9 that is above the right triangular region with vertices (0, 0), (1,0) and (1, 2). (i) Write down the vector function r(r, y) and domain of the parameterization for surface M. (ii) For the vector field F ri+yj+ (2 + y) k, evaluate F. M (iii) For the scalar function g(x, y, z) = xz, set up but do not evaluate an iterated double integral that gives the surface integral of g over M.
Expert Solution
steps

Step by step

Solved in 4 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS