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(5 points) Stokes' Theorem is a deep mathematical theorem that relates a line integral along a boundary of an oriented surface in 3-space to a

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(5 points) Stokes' Theorem is a deep mathematical theorem that relates a line integral along a boundary of an oriented surface in 3-space to a flux integral across the oriented surface. The orientation on the boundary is inherited from the orientation on the surface. Use Stokes' Theorem to solve the following problem. Consider the vector field I? = (xy, yz, xz). Let the surface S be the piece of the surface 2 = 25 x2 directly above the rectangle 0 5 x 5 5 and 3 S y S 3. Suppose S is oriented upward, and let C be the boundary of the surface S, with the inherited orientation. You might want to think about how the surface looks. Find the line integral below. [CF-diet]

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