Stokes’ Theorem for evaluating line
14. F = 〈x2 – y2, z2 – x2, y2 – z2〉; C is the boundary of the square |x| ≤ 1, |y| ≤ 1 in the plane z = 0.
Want to see the full answer?
Check out a sample textbook solutionChapter 14 Solutions
Calculus: Early Transcendentals (2nd Edition)
Additional Math Textbook Solutions
Thomas' Calculus: Early Transcendentals (14th Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Precalculus (10th Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Calculus and Its Applications (11th 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_forwardCalculate line integral p F.dr where F(x,y) (7x + y, 5x + 2y) and C is a rectangle with vertices (0, 2), (8, 2), (8, 5) and (0, 5) oriented clockwise.arrow_forwardPlease help solve for the problem provided in the photo belowarrow_forward
- Use Green's Theorem to evaluate the following integral Let² dx + (5x + 9) dy Where C is the triangle with vertices (0,0), (11,0), and (10, 9) (in the positive direction).arrow_forwardChannel flow The flow in a long shallow channel is modeled by the velocity field F = ⟨0, 1 - x2⟩, where R = {(x, y): | x | ≤ 1 and | y | < 5}.a. Sketch R and several streamlines of F.b. Evaluate the curl of F on the lines x = 0, x = 1/4, x = 1/2, and x = 1.c. Compute the circulation on the boundary of the region R.d. How do you explain the fact that the curl of F is nonzero atpoints of R, but the circulation is zero?arrow_forwardX Incorrect. Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. fy²dx + 5x dx + 5x²dy, where C is the square with vertices (0, 0), (3, 0), (3, 3), and (0, 3) oriented counterclockwise. y²dx + 5x²dy i 0 eTextbook and Mediaarrow_forward
- Describe and sketch the surface given by the function.arrow_forwardEvaluate | F dr where C is the intersection of the surfaces y = x and z = x' from the origin to (1,1,1) and C F =(xy) i +(yz)j +(xz) k .arrow_forward2.Proof that any tangent plane for the surface F( F) point = 0 passses through a fixedarrow_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