MTH 255 Lecture 11: 02012019
10 Feb 2019
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C is a closed simple curve that is piecewise smooth ( so. C is the oriented boundary of a connected and simply connected region. I i ( used to find info about region , or find into about. R as in the theorem and vector field. , g > having continuous partial derivatives then. Claim i tf - fey da = # pdx. If - ffs da tabled - ffydlt]dx= - lab [ plx , d ) pix. , c) tax fab [ pix , a. & pdx = f pdx t f pdx top bottom x is constant on the vertical sides. Jab pix , c) dx t ( x , d) R can rectilinear boundary it suffices be to approximated arbitrarily closely by regions with show. Any region with a rectilinear boundary can be partitioned into rectangles. I or a piece of a side then there is a cancellation of the integral along the shared side :
