ok, so I dont know how to draw integration signs on this thing if it is possible, but let me try to ask the question anyway.
So Green's Theorem is :
line integral on closed curve C (M dx + N dy) = double integral on region R [(dN/dx - dM/dy) dA]
So, based on this, we can show that:
double integral on region R (dA) = 1/2 * line integral on closed curve C (-y dx + x dy)
Ok. I get that part, but then they say that it follows obviously that:
double integral on region R (dA) =
line integral on closed curve C (-y dx) =
line integral on closed curve C (x dy)
I dont see why this has to be true. Can someone explain it to me please. Thanks.
If anyone has the book, what I'm talking abt is in the Princeton Review Book on page 153 in the 3rd Ed and I'm not sure if its on a diff page or what in any other edition.