Use Stokes' Theorem to evaluate ?_C F · dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = xyi + yzj + zxk, C is the boundary of the part of the paraboloid z = 1 - x^2 - y^2 in the first octant.
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We can parameterize this surface as follows: r(u, v) = <u, v, 1 - u^2> for 0 ≤ u ≤ 1, 0 ≤ v ≤ sqrt(1 - u^2) Show more…
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