Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F = 4zi + xj + 4yk across the surface S: r(r,0) =r cos Oi +r sin Oj + (16 -) k, Osrs4,0<0<2n in the direction away from the origin. .....
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- Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F across the surface S in the direction away from the origin. F= 5yi + (5 - 5x)j + (z² - 2)k S: r(), 0) = (V5 sin p cos e) i+ (V5 sin o sin 0) j+ (V5 cos 4) k, 0 spst/2,0s0s2a The flux of the curl of the field F across the surface S in the direction of the outward unit normal n is (Type an exact answer, using t as needed.)Find the circulation and flux of the field F= - xi - yj around and across the closed semicircular path that consists of the semicircular arch r, (t) = (a cos t)i + (a sin t)j, Ostsn, followed by the line segment r2 (t) = ti, -astsa.Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F = 5zi + xj + 2yk across the surface S: r(r,0) =r cos Oi +r sin 0j + (25 -) k, 0srs5, 0s0s2n in the direction away from the origin. The flux of the curl of the field F is (Type an exact answer, using n as needed.)
- 2. Find the curl of the vector field. F = z°e* sin(2 y)i – e' cos yj+ xyzk toFind the curl of the vector field F (5y cos(r), 2r sin(y)). curl F =Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F across the surface S in the direction away from the origin. F= 4yi + (5 - 5x)j + (z - 2)k S: r(), 0) = (V7 sin o cos 0) i+ (17 sin o sin 0) j+ (V7 cos o) k, 0Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F = 4zi + 5xj + 5yk across the surface S: r(r,0) =r cos ei +r sin ej + (9-r)k, 0srs3, 0s0<2n in the direction away from the origin. The flux of the curl of the field F is (Type an exact answer, using a as needed.)Recommended textbooks for youAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage