2-6 Use Stokes' Theorem to evaluate is curl F dS. 2. F(x, y, z) = x2 sin z i + y 2 j + xy k, y that lies S is the part of the paraboloid z1 above the xy-plane, oriented upward 3, F(x, y, z) ze i + x cos y j + xz sin y k, S is the hemisphere x2 + y2 + z2 = 16, y the direction of the positive y-axis 0, oriented in 4. F(x, y, z) tan-i (xyz?) i + x2yj + x":-k, S is the cone x-v/y2 + Z2, 0 direction of the positive x-axis 2, oriented in the 5, F(x, y, z) = xyz i + xy j + x2yz k, S consists of the top and the four sides (but not the bottom) of the cube with vertices (+1, +1, t1), oriented outward 6. F(x, y, z) = e"i + ex: j + x": k, S is the half of the ellipsoid 4x2 y +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 c F dr. In each case is oriented counterclockwise as viewed from above. 7. F(x, y, z) = (x + y*) i + (y + z?) j + (z + x*) k, C is the triangle with vertices (1,00 0
