Area of a Small Loop of a Lemniscate

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Homework Statement



Small loop of r=1+2sin2(theta)

Homework Equations



integral of .5[f(theta)]2 d(theta)

The Attempt at a Solution



I cannot figure out what the limits of integration are.
 
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find the maxima and minima of the curve in the range 0 to 2pi

the minima will tell you about the small loop, find the value of theta for which f(theta) = 0 preceding and succeding the minima

those are your limits
 
Here's what I did- use a graphing calculator, set to "polar" mode, and play with the window.
 
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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