Thread: Area and Arc Length of |y|^n+|x|^n=a^n

I've been trying to fing both the area and the arc length of
$\displaystyle |y|^n+|x|^n=a^n$
with respect to x where a and n are constants

Graphing examples of the function as well as solving simple examples where a=1 and n=1 (diamond) or n=2 (circle) has shown that the graph is symetrical in all quadrants.

I've written the in equation terms of y and set limits to account for the symetry and have gotten.
$\displaystyle A(x)=4 \int_0^a (a^n-x^n)^{(1/n)}$
for the area and
$\displaystyle L(x)=4 \int_0^a \sqrt{1+(d/dx(a^n-x^n)^{(1/n)})}$
But I do not how to procede from there.

I think the power of the integral becomes (n+1)/n but i don't know how to handle the (a^n-x^n) portion

Anyone? I still can't figure it out.