MHB Evaluating Complex Integration I_c |z^2|

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To evaluate the integral I_c |z^2| over the square with vertices at (0, 0), (1, 0), (1, 1), and (0, 1), a parametrization of the square is essential for computing the path integral. The square can be divided into four line segments, each defined by specific equations: from (0, 0) to (1, 0), (1, 0) to (1, 1), (1, 1) to (0, 1), and (0, 1) to (0, 0). The integral can be evaluated by substituting the parametrization into the integral and calculating along each segment. The discussion emphasizes the necessity of defining these lines and their corresponding limits for proper evaluation. Understanding these components is crucial for accurately computing the integral.
AkilMAI
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How can I evaluate I_c |z^2|,where I is the integral and c is the square with vertices at (0, 0), (1, 0), (1, 1), (0, 1) traversed anti-clockwise...?
 
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Did you write a parametrization of this square?
 
how will that help?
 
It's needed to compute a path integral.
 
ok ...how should I proceed?
 
James said:
ok ...how should I proceed?

What would be the equation of the four lines that make the square, and between which values are these lines defined?
 
max(x^2,y^2) with sides of 1?
 

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