Green's Theorem as a Fundamental Theorem of Calculus Show that if the circulation form of Green's f(x)' Theorem is applied to the vector field ( 0,). where c > 0 and R = {(x, y): a SIS b,0 s ys c}, then the result is the Fundamental Theorem of Calculus, dx = f(b) – f(a).

V x (A(x, y, z)VB(x,y, z)) = VB × VA where A and B are differentiable scalar functions of x, y, and z. You can look in a table of vector calculus identities and check easily enough whether my assertion is true. But don't just cite the table. Instead, do one (1) of the following: • Derive the identity for arbitrary functions A and B (thus proving my assertion true). • Derive some different identity for V x (AVB) (thus proving my assertion false). • Give me functions A and B for which my assertion does not hold. You don't have to do more than one of those things. Just one (1) will suffice.