I'm attempting to find the area enclosed by the graph $x^4 + y^4 = 1$ as shown below.
My approach was to rearrange the equation so it is in terms of $y = f(x)$ and integrate one of the top two quadrants with respect to $x$ and then multiply by $4$ to get the area for the whole shape. I've never tried to integrate this kind of graph before and I'm not sure If I've done it correctly. Any input or assistance would be much appreciated. Thanks.