Trying to solve for the area enclosed by $x^4+y^4=1$. A friend posed this question to me today, but I have no clue what to do to solve this. Keep in mind, we don't even know if there is a straightforward solution. I think he just likes thinking up problems out of thin air.

Anyway, the question becomes more general, since we *think* that

$lim_{n\to\infty}\int_0^1{(1-x^n)^{1/n}} = {1\over4}$ (it approaches a square / becomes linear)

can anyone confirm that this is true or not?