September 10th, 2017, 10:37 AM  #11 
Member Joined: May 2017 From: Slovenia Posts: 87 Thanks: 0  
September 10th, 2017, 12:18 PM  #12 
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,410 Thanks: 715  
September 10th, 2017, 10:16 PM  #13 
Member Joined: May 2017 From: Slovenia Posts: 87 Thanks: 0  
September 10th, 2017, 11:32 PM  #14 
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,410 Thanks: 715  The integration curve is an ellipse, the surface an elliptical disk. The extremes are the max and min values the coordinates along the ellipse. In defining the surface we have $1 \leq u \leq 1,~1\leq v \leq 1$ by design. This corresponds to $\rho \in [0,1]$ Take a look at the curve/surface in some graphing software and it should become clear. 

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stoke, stuck, theorem 
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