in On 12. (a c Stokes' Theorem to evaluate JJ curl F . dS. (. y. z) = x'sinzity"j+ xyk, the part of the paraboloid z = 1 - x2 - y? that lies Have the xy-plane, oriented upward 7 2) = ze" i + x cosy j + xz sink, the hemisphere x2 4 y + 22 - 16, > > 0, oriented in airection of the positive y-axis 13- fie " y z) = tan (x2 yz? ) i+ xzyj + x222k, get the cone x = Vy2 + 22, 0 x - 2, oriented in the 13 direction of the positive x-axis B. P( x. y. 2 ) = xyzi + xy j + x2yzk, S consists of the top and the four sides (but not the bottom) of the cube with vertices (+1, +1, +1), oriented outward 6. F(x, y, z) = ety it exj + x2zk, S is the half of the ellipsoid 4x2 + y2 + 4z2 = 4 that lies to the right of the xz-plane, oriented in the direction of the positive y-axis 7-10 Use Stokes' Theorem to evaluate Jc F . dr. In each case C is oriented counterclockwise as viewed from above. F (x, y, z) = ( x + y2) i + (y + z2) j + (z+ x2) k, C is the triangle with vertices (1, 0, 0), (0, 1, 0), and (0, 0, 1) 8. F(x, y, z) = i + ( x + yz) j + (xy - vz) k, C is the boundary of the part of the plane 3x + 2y + z = 1 in the first octant 9. F(x, y, z) = xyi + yzj + zxk, C is the boundary of the part of the paraboloid z = 1 - x2 - y in the first octant