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.