Stokes’ Theorem for evaluating line
16. F = 〈2xy sin z, x2 sin z, x2y cos z〉; C is the boundary of the plane z = 8 – 2x – 4y in the first octant.
Want to see the full answer?
Check out a sample textbook solutionChapter 14 Solutions
Calculus: Early Transcendentals (2nd Edition)
Additional Math Textbook Solutions
Elementary Statistics (13th Edition)
Elementary Statistics
Pre-Algebra Student Edition
Algebra and Trigonometry (6th Edition)
College Algebra (7th Edition)
Elementary Statistics: Picturing the World (7th Edition)
- c) Verify Stokes's Theorem for F = (x²+y²)i-2xyj takes around the rectangle bounded by the lines x=2, x=-2, y=0 and y=4arrow_forwardCalculate 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_forwardFind a parametrization of the surface z = 3x² + 8xy and use it to find the tangent plane at x = 1, y = 0, z = 3. (Use symbolic notation and fractions where needed.) z =arrow_forward
- Find the surface area of the "Coolio McSchoolio" surface shown below using the formula: SA = integral, integral D, ||ru * rv||dA %3D The parameterization of the surface is: r(u,v) = vector brackets (uv, u + v, u - v) where u^2 + v^2 <= 1 A.) (pi/3)(6squareroot(6) - 8) B.) (pi/3)(6squareroot(6) - 2squareroot(2)) C.) (pi/6)(2squareroot(3) - squareroot(2)) D.) (pi/6)(squareroot(6) - squareroot(2)) E.) (5pi/6)(6 - squareroot(2))arrow_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(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_forward
- Evaluate 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(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_forwardREFER TO IMAGEarrow_forward
- 5. 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_forwardDetermine the type of points on the X (u, v) = (u, v, u?) surface. Differential geometryarrow_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