Verify Stokes' Theorem for the given vector field and surface, oriented with an upwardpointing normal.

\(\mathbf{F}=\left\langle e^{y-z}, 0,0ightangle\), the square with vertices \((1,0,1),(1,1,1),(0,1,1)\), and \((0,0,1)\)

Transcribed Image Text:

THEOREM 1 Stokes' Theorem Let S be a surface as described earlier, and let F be a vector field whose components have continuous partial derivatives on an open region containing S. as F.dr = JG Ils The integral on the left is defined relative to the boundary orientation of S. If S is a closed surface, then curl(F). ds curl(F) dS=0 1