Concept explainers
Verifying Stokes’ Theorem Verify that the line
9. F = 〈y – z, z – x, x – y〉; S is the cap of the sphere x2 + y2 + z2 = 16 above the plane
Learn your wayIncludes step-by-step video
Chapter 14 Solutions
Calculus: Early Transcendentals (2nd Edition)
Additional Math Textbook Solutions
University Calculus: Early Transcendentals (3rd Edition)
Glencoe Math Accelerated, Student Edition
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
Calculus and Its Applications (11th Edition)
- A. Let F = P i + Q j be a smooth vector field on R^2 , C a closed simple curve in R^2 , and D the plane simple region enclosed by C. State Green’s Theorem for F, C, and D. B. Evaluate the line integral in Green’s Theorem when F = (x + y)i + xy j and C is the unit circle with equation x^2 + y^2 = 1. C. Evaluate the double integral in Green’s Theorem when F = (x + y)i + xy j, C is the unit circle with equation x 2 + y 2 = 1, and D is the unit disc bounded by C. Then compare your answers in Parts B and C.arrow_forwardEvaluate the surface integral ∬ F ⋅ dS for the given vector field F and the oriented surface S . In other words, find the flux of F across S . For close surfaces, use the positive (outward) orientation.Solve using ∬ F ⋅ dS = ∬ F ⋅ n dS = ∬ F ⋅ (ru x rv) dA method and explain your parametrization and orientation reasoning. F(x, y, z) = yi + (z - y)j + xkS is the surface of the tetrahedron with vertices (0, 0, 0) (1, 0, 0) (0, 1, 0) and (0, 0, 1)arrow_forwardEvaluate the surface integral ∫∫S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = y i + (z-y) j + x k S is the surface of the tetrahedron with vertices (0, 0, 0), (1, 0, 0), (0, 1, 0), and (0, 0, 1).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