This problem has me stumped because I can't figure out how to find the area of the region. I got an integral, but I don't know how to evaluate it. Here's the problem:(adsbygoogle = window.adsbygoogle || []).push({});

Find the area of the region bounded by the graph of [tex]y^2 = x^2 - x^4[/tex].

I solved the equation for y and got [tex]y = \pm\sqrt{x^2 - x^4}[/tex].

If I graph it, it looks like a bow tie with four symmetrical regions, so I decided to find the area of the top-right region. Here's the integral I came up with:

[tex]\int_{0}^{1} \sqrt{x^2 - x^4} dx[/tex].

That's all well and good I guess, but I have no idea how to evaluate that integral! As far as I know, I don't yet have the calculus knowledge to solve that type of integral. Should I solve for x and put the integral in terms of y?

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# Find the area of the region

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