Concept explainers
Stokes’ Theorem for evaluating line
11. F = 〈2y, –z, x〉; C is the circle x2 + y2 = 12 in the plane z = 0.
Learn your wayIncludes step-by-step video
Chapter 17 Solutions
Calculus: Early Transcendentals, Books a la Carte, and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition)
Additional Math Textbook Solutions
Glencoe Math Accelerated, Student Edition
University Calculus: Early Transcendentals (4th Edition)
Precalculus (10th Edition)
Precalculus Enhanced with Graphing Utilities (7th Edition)
University Calculus: Early Transcendentals (3rd Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
- REFER TO IMAGEarrow_forwardEvaluate the circulation of G = xyi+zj+7yk around a square of side 9, centered at the origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive x-axis. Circulation = Prevs So F.dr-arrow_forwardEvaluate the circulation of G = xyi + zj + 4yk around a square of side 4, centered at the origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive x-axis. Circulation = Jo F. dr =arrow_forward
- Calculate the curl(F) and then apply Stokes' Theorem to compute the flux of curl(F) through the surface of part of the cone √x² + y2 that lies between the two planes z = 1 and z = 8 with an upward-pointing unit normal, vector using a line integral. F = (yz, -xz, z³) (Use symbolic notation and fractions where needed.) curl(F) = flux of curl(F) = [arrow_forwardEvaluate the line integral PF • dr by evaluating the surface с integral in Stokes' Theorem with an appropriate choice of S. Assume that C has a counterclockwise orientation when viewed from above. F = (-3y, -z,x) C is the circle x² + y² = 26 in the plane z = 0.arrow_forwardmaths 1819arrow_forward
- (c) Verify the line integral and surface integral by relating them to the Stokes' Theorem where C is the circle x² + y² 1 on xy-plane with a counterclockwise orientation looking down the positive z-axis. = √ x²ydx + xdyarrow_forward5. Use Stokes' Theorem (and only Stokes' Theorem) to evaluate F dr, where F(r, y, z) be clear, if you want to evaluate this and use Stokes' Theorem then you must be calculating the surface integral of the curl of F of a certain surface S.) (3y,-2x, 3y) and C is the curve given by a +y? = 9, z = 2. (So to %3Darrow_forwardStokes’ Theorem for evaluating surface integrals Evaluate the line integral in Stokes’ Theorem to determine the value of the surface integral ∫∫S (∇ x F) ⋅ n dS. Assume n points in an upward direction. F = ⟨4x, -8z, 4y⟩; S is the part of the paraboloidz = 1 - 2x2 - 3y2 that lies within the paraboloid z = 2x2 + y2 .arrow_forward
- Set-up the integral being asked in the problem. No need to evaluate. Show all solutions.arrow_forward(5) , Use Stokes' Theorem to find the line integral / (x + 2y*)ï+ (y + z²)j+(z+ 2r*)k) • dï - 2r*)E) · dr where C is the boundary of the triangle T with vertices (1,0, 0), (0, 1, 0), (0, 0, 1) and oriented counter-clockwise when viewed from above.arrow_forwardhow do i solve the attached calculus problem?arrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning