Stokes’ Theorem on closed surfaces Prove that if F satisfies the conditions of Stokes’ Theorem, then
Want to see the full answer?
Check out a sample textbook solutionChapter 17 Solutions
Calculus: Early Transcendentals (3rd Edition)
Additional Math Textbook Solutions
University Calculus: Early Transcendentals (4th Edition)
Glencoe Math Accelerated, Student Edition
University Calculus: Early Transcendentals (3rd Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
- Stokes’ Theorem on closed surfaces Prove that if F satisfies theconditions of Stokes’ Theorem, then ∫∫S (∇ x F) ⋅ n dS = 0,where S is a smooth surface that encloses a region.arrow_forwardClairaut's Theorem Let DCR? be a disk containing the origin and assume that g : D R is a function given by g(x, y) = e" (cos y +r sin y). Prove that g(x, y) satisfies the Clairaut Theorem at point (0, 0).arrow_forwardClairaut's Theorem Let DCR be a disk containing the origin and assume that q : D → R is a function given by g(x, y) = e" (cos y +x sin y). Prove that g(x, y) satisfies the Clairaut Theorem at point (0, 0).arrow_forward
- Clairaut's Theorem Let DC R? be a disk containing the origin and assume that g : D→ R is a function given by g(x, y) = e" (cos y + x sin y). Prove that g(x, y) satisfies the Clairaut Theorem at point (0,0).arrow_forwardClairaut's Theorem Let DC R?be a disk containing the origin and assume g : D → R is a function given by that g(x,y) = e" (cos y + xsin y). Prove that g(x,y) satisfies the Clairaut Theorem at point (0,0).arrow_forwardUse Stokes’ Theorem to evaluate ∫ F*dr where C is oriented counter-clockwise as viewed from above. F(x,y,z) = yi-zj+x2k C is the triangle with vertices (1,0,0), (0,1,0), and (0,0,1) Note: The triangle is a portion of the plane x+y+z=1arrow_forward
- Use Stokes' Theorem to evaluate Use Stokes' Theorem to evaluate ∫C F · dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = yzi + 3xzj + exyk, C is the circle x2 + y2 = 4, z = 6.arrow_forward(ii) Use Stokes' Theorem to evaluate F. dr, where F(x, y, z) = x²zi + xy²j + z²k and C is the curve of intersection of the plane x+y+z = 1 and the cylinder x² + y² = 9, oriented counterclockwise as viewed from above. 5 z 0+ -2 y 0arrow_forwardSketch the surface of f(x,y)arrow_forward
- aut's Theorem Let DC R? be a disk containing the origin and assume that g : D → R is a function given by g(x, y) = e" (cos y + x sin y). Prove that g(x, y) satisfies the Clairaut Theorem at point (0, 0).arrow_forwardlus III 1Unit Use Stokes's Theorem to evaluate F. dr where C is oriented counterclockwise as viewed from above, F(x, y, z) =, C is the circle x2 + y? = 4, and z = 4.arrow_forwardUsing Green’s theorem, evaluate the line integral ∮Cxydx+ (x+y)dy, where C is the curve bounding the unit disk R.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