Let f:U → R2 be a function of class Co in the open U CR2 Define the function J(, y) = det f'(x, y) for all (x,y) EU. Sup

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Let F U R2 Be A Function Of Class Co In The Open U Cr2 Define The Function J Y Det F X Y For All X Y Eu Sup 1 (221.26 KiB) Viewed 59 times

Let f:U → R2 be a function of class Co in the open U CR2 Define the function J(, y) = det f'(x, y) for all (x,y) EU. Suppose that DCU is a compact domain whose boundary aD is a closed smooth curve. If f(x, y) = 0 for all read, prove that: S S J(r, y)dxdy = 0.