Using Stokes' theorem, solve the line integral of G(x, y, z) - (1, x + yz, xy-√z) around the boundary of surface S, which is given by the piece of the plane 3x + 2y + z = 1 where x, y, and z all ≥ 0.
Using Stokes' theorem, solve the line integral of G(x, y, z) - (1, x + yz, xy-√z) around the boundary of surface S, which is given by the piece of the plane 3x + 2y + z = 1 where x, y, and z all ≥ 0.
Using Stokes' theorem, solve the line integral of G(x, y, z) - (1, x + yz, xy-√z) around the boundary of surface S, which is given by the piece of the plane 3x + 2y + z = 1 where x, y, and z all ≥ 0.
Using Stokes' theorem, solve the line integral of G(x, y, z) - (1, x + yz, xy-√z) around the boundary of surface S, which is given by the piece of the plane 3x + 2y + z = 1 where x, y, and z all ≥ 0.
Transcribed Image Text:Stokes' Theorem Let S be an oriented piecewise-smooth surface that is
bounded by a simple, closed, piecewise-smooth boundary curve C with positive
orientation. Let F be a vector field whose components have continuous partial
derivatives on an open region in R³ that contains S. Then
S.F.
r=ff cu
F. dr
curl F. ds
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
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