- #1

- 159

- 0

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?