Solving a Mysterious Double Integral: Help Needed!

Lorenc
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Hey guys, how are you? I was studying for my calculus final and stumbled upon a peculiar function. Now I have to find the area bounded by the function (x^2+y^2)^3=xy^4 using a double integral. Now, the problem is that the graph is totally unknown to me (I have some ideas but I am not shure). A substitution with u and v, doesn't seem to work and going to polar doesn't work either :/ Maybe I am doing something wrong, I don't know. Can anybody help me? Thank you in advance :)
 
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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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