Converting polar to cartesian coordinates

bobsmith76
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Homework Statement



Screenshot2012-02-16at15012AM.png


Homework Equations



Screenshot2012-02-16at15136AM.png


The Attempt at a Solution



Do you see that 2 between A and the integral? There's no 2 in the above equation. I don't see where that 2 came from. Everything else is fine.
 
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The 2 comes from the symmetry. 0 to pi/4 on the sine circle is only calculating the bottom-right half of the area.
 
because if you just did it with no 2*the integral then you would only get the area of half of your region
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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