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11. Let I = ( F . dr, where F(x, y) = (y + sinx2, x2 + ey ) and C is the circle of radius 4 centered at the origin. Which is easier, evaluating / directly or using Green's Theorem? Evaluate / using the easier method. 12. Use o y dr to compute the area of the ellipse (x/a) + (y/b)? = 1. 13. Let F = (0, -z, 1). Let S be the spherical cap a + y' + z? 1/2. Evaluate F . dS directly. Then verify that F is the curl of A = (0, x, x2) and evaluate the surface integral again using Stokes' theorem. 14. Calculate the curl of F = (e - y, e + x, cos(xz)) and apply Stokes' theorem to compute the flux of curl(F) through the upper half of the unit sphere with outward pointing normal. 16. Verify that the Divergence theorem holds for F(x, y, z) = (2x, 3z, 3y) over the region a + y