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Verify that the line integral and the surface integral of Stokes' Theorem are equal for the following vector field, surface S, and closed curve C. Assume that C has counterclockwise orientation and S has a consistent orientation. F = (y - z,z - x, x - y) ; S is the cap of the sphere x + y+ z =36 above the plane z= v11 and C is the boundary of S. Construct the line integral of Stokes' Theorem using the parameterization r(t) = (5 cost, 5 sint, V11 ), for Osts 2x for the curve C. Choose the correct answer below. 27t O A. (- 25 +51/17 sint + 51/11 cost) at O B. (5V11 sint + 51/11 cost) at O c. (25 -5171 sint- 5171 cost) dt O D. (-5171 sint-5V11 cost) dt ... Screen Shot 2022-12-11 at 9.40.00 PM Q Q A Q Q Search Evaluate the line integral OF . dr by evaluating the surface integral in Stokes' Theorem with an appropriate choice of S. Assume that C has a counterclockwise orientation when viewed from above. F = (7y, - Z,x) C is the circle x2+ y =22 in the plane z = 0. Rewrite the given line integral as an area integral over the appropriate region of the xy-plane. SF. ar = SS (D) dA Evaluate the line integral OF . dr by evaluating the surface integral in Stokes' Theorem with an appropriate choice of S. Assume that C has a counterclockwise orientation when viewed from above. F= (x2 - y2,z2 -x2, y2 - z2) C is the boundary of the square |x| $ 10, ly| s 10 in the plane z = 0. Rewrite the given line integral as an area integral over the appropriate region of the xy-plane. OF . ar = JJ() dA C R