Stoke's Theorem: 2. Evaluate the flux integral curl FdS by use of Stoke's Theorem: F(x, y, z) = (y², zy, zz), where S is the hemisphere r² + y²+z² = 1, z0, and is the "outward pointing" unit normal (Hint: First use Stoke's Theorem to convert the flux integral into a circulation integral). 3. Evaluate the flux integral ffs curl F.ñdS by use of Stoke's Theorem: F(x, y, z)=(y-z, yz,-12), where S is the five faces of the cube 0

Use Stokes' Theorem to evaluate curl F- dS where F(r, y, 2) = 4ryzi – ryj + x?yzk and S consists of the top and the four sides (but not the bottom) of the cube with vertices (+2, ±2, +2), oriented outward. Since the box is oriented outwards the boundary curve must be transversed ? v when viewed from the top. A parametrization for the boundary curve C seen below from above can be given by: rT(t) rL(t) FR(t) rB(t) rz(t) = ( Σ Σ Σ 0