MATH 322 Lecture : Integral formulas for area
2 Dec 2011
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During class, i gave the following formula for calculating the area a inside a closed, positively-oriented, contour c: The text gives the following formula in exercise 7, page 163: (1) (2) Well, i derived equation (1) in class, and so it must be correct. To see what"s wrong with equation (2), let"s split the integral into its real and imaginary parts z dz = x + iy, so that equation (1) becomes. So it is only the real part of equation (2) that corresponds to the area enclosed by the contour c.
