Verify that the line integral and the surface integral of Stokes' Theorem are equal for the following vector field, surf

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Verify That The Line Integral And The Surface Integral Of Stokes Theorem Are Equal For The Following Vector Field Surf 1 (518.45 KiB) Viewed 22 times

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. 2 2 2 2 F= (y, - x, 7); S is the upper half of the sphere x + y + z = 9 and C is the circle x + y = 9 in the xy-plane. 2 Construct the line integral of Stokes' Theorem using the parameterization r(t) = (3 cos t, 3 sin t,0), for Osts 2n for the curve C. Choose the correct answer below. 21 O A. joa 9 dt 21 B. -9 9dt 0 211 OC. s 18dt 0 21 D. S-1 18 dt n