1.

Find the flux of the vector field F= (e- X,3z,3xy) across the curved sides of the surface S = {(x,y,z): z= cosy, ly| Sx, 0Sx53) . Normal vectors point upward. . . . Set up the integral that gives the flux as a double integral over a region R in the xy-plane. IS Finds = ]](D dA R (Type exact answers.)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, - x - z,y - x) ; S is the part of the plane z =7 -y that lies in the cylinder x2 + y2 = 16 and C is the boundary of S. Construct the line integral of Stokes' Theorem using the parameterization r(t) = (4 cost,4 sin t,7 - 4 sin t) , 0St2x, for C. Choose the correct answer below. O A. (16 cos 2t -28 sint) at B. (16 sin 2t - 28 cost) dt 0 O c. (28 cost - 16 sin 2+) at 0 2 x O D. (28 sint - 16 cos 2+) at 0 Construct the surface integral of Stokes' Theorem using R = {(x, y): x + y's 16} as the region of integration. Choose the correct answer below. 21 4 CA. S frdr de 0 0 21 4 O B. S S -2r ar de 0 0 21 4Evaluate both integrals to verify that they are equal. What is the result? E (Type an exact answer, using 1: as needed.)