Use Stokes’ Theorem to evaluate
Trending nowThis is a popular solution!
Chapter 16 Solutions
CALCULUS FULL TEXT W/ACCESS >CI<
- Let F = (3z + 3x²) ¿+ (6y + 4z + 4 sin(y²)) 3+ (3x + 4y + 6e²²) k (a) Find curl F. curl F - (b) What does your answer to part (a) tell you about SF. dr where C' is the circle (x − 15)² + (y – 10)² = 1 in the xy-plane, oriented clockwise? ScF. dr = 0 (c) If C is any closed curve, what can you say about ScF. dr? SoF. dr = 0 (d) Now let C be the half circle - (x − 15)² + (y − 10)² = 1 in the xy-plane with y > 10, traversed from (16, 10) to (14, 10). Find SF. dr by using your result from (c) and considering C plus the line segment connecting the endpoints of C. -0 Lc F. dr =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_forwardPlease help mearrow_forward
- Please solve the screenshot (handwritten preferred) and explain your work, thanks!arrow_forwardUse Stokes' theorem to evaluate Ĝ - dĩ, vhere Ğ(1, Y, 2) = (2r, y,0) and D is any closed curve.arrow_forwardEvaluate fS (3x + 4y²)dA by changing it into polar coordinates over the region in upper half plane bounded by the circles x? + y² = 1 and x2 + y² = 4. ww MMMMarrow_forward
- Evaluate the circulation of G = xyi+zj+7yk around a square of side 9, centered at the origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive x-axis. Circulation = Prevs So F.dr-arrow_forward> Let F =< x²e³², xez, z²exy :// curl F. dS, where S Use Stokes' Theorem to evaluate S is the hemisphere x² + y² + z² = 1, z ≥ 0, oriented upwardsarrow_forwardLet F =. Compute the flux of curl(F) through the surface z = 1- x² - y² for x² + y² ≤ 11 oriented with an upward-pointing normal. Flux = help (fractions) (Use symbolic notation and fractions where needed.) Hint: Stokes' Theorem shows a direct computation can be done in an alternative fashion.arrow_forward
- Let F = (3z + 3x²) i + (6y + 4z + 4 sin(y²)) 3+ (3x+4y+6e²²) k (a) Find curl F. curl F = (b) What does your answer to part (a) tell you about SF. dr where C is the circle (x − 15)² + (y − 10)² = 1 in the xy-plane, oriented clockwise? ScF·dr = 0 (c) If C is any closed curve, what can you say about ScF. dr? ScF-dr = 0 (d) Now let C be the half circle (x − 15)² + (y – 10)² = 1 in the xy-plane with y > 10, traversed from (16, 10) to (14, 10). Find SF. dr by using your result from (c) and considering C plus the line segment connecting the endpoints of C. ScF·dr = 0arrow_forwardUse Stokes' Theorem to evaluate curl F· dS. F(x, y, z) = tan-1(x²yz²)i + x?yj + x²z²k, S is the cone x = V y? + z?, 0 < x< 4, oriented in the direction of the positive x-axis.arrow_forwardVerify the Stokes' Theorem in evaluating F.dr if F(x, y, z) = z² i + 2xj-y³k, where C is the circle x² + y² = 1 in xy-plane with the counterclockwise orientation looking down the positive z-axis.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage