Concept explainers
Stokes’ Theorem for evaluating line
13. F = 〈x2 – z2, y, 2xz〉; C is the boundary of the plane z = 4 – x – y in the first octant.
Learn your wayIncludes step-by-step video
Chapter 14 Solutions
Calculus: Early Transcendentals (2nd Edition)
Additional Math Textbook Solutions
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
College Algebra with Modeling & Visualization (5th Edition)
College Algebra (7th Edition)
Elementary Statistics
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
Elementary Statistics (13th Edition)
- Stokes’ 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_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_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_forward
- Set-up the integral being asked in the problem. No need to evaluate. Show all solutions.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_forwardM2arrow_forward
- Cal 3arrow_forwardEvaluate the line integral (ci+ 3xyj – (x + z)k) · dr where C is the parametric curve r(t) = (1 – t)i + (4 + t)j + (2 – t)k, 0arrow_forwardi+z i and w = transform w<1 into the lower half Show that both the transforms w = i- z plane Im( z) <0.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- 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