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Stokes’ Theorem for evaluating surface
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- 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 = ⟨ex, 1/z, y⟩; S is the part of the surface z = 4 - 3y2 thatlies within the paraboloid z = x2 + y2.arrow_forwardFirnd the area of the surface of the half cylinder {(r,0,z): r=6, 0s0S1, 0SzS5} using a parametric description of the surface. Set up the integral for the surface area using the parameterization u=0 and v=z. !! S SO du dv (Type an exact answers, using x as needed.) The surface area is (Type an exact answer, using x as needed.)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.arrow_forward
- Evaluate the surface integral. J y ds, S is the helicoid with vector equation r(u, v) = (u cos(v), u sin(v), v), 0sus 6,0 SV SR. [(10) ()-1] Need Help? Read It Watch Itarrow_forwardVerify Stokes' theorem. Assume that the surface S is oriented upward. F=3zi−5xj+2yk; S that portion of the paraboloid z=36−x^2−y^2 for z≥0 I'm having trouble finding the normal n*dS in Stokes's Theoremarrow_forwardFur Find the area of the surface. Syr The helicoid (or spiral ramp) with vector equation r(u, v) = u cos(v) i + u sin(v) j + v k, 0 s u s 1, 0 s vs 5x.arrow_forward
- Describe and sketch the surface given by the function. f(x, y) = e−xarrow_forwardFine the area of the surface obtained by the rotating the following curve about the x-axis. (The interval is provided in the image.)arrow_forwardWhat is a unit normal to the surface x?y + 2xz = 4 at the point (2, –2, 3) O+3+歌arrow_forward
- Evaluate the surface integral SG(x,y,z) do using a parametric description of the surface. S G(x,y,z) = z², over the hemisphere x² + y² + z² = 4, zz0 The value of the surface integral is. (Type an exact answer, using as needed.)arrow_forwardEvaluate the surface integral | G(x.y.z) do using a parametric description of the surface. G(x.y.z) = 2z, over the hemisphere x +y° +z? = 36, z20 The value of the surface integral is (Type an exact answer, using 1 as needed.)arrow_forwardClassify and sketch the surface x − y2 − 4z2 = 0.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
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