Question: Squircle areas: why does int give so lousy values?

( squircle is the humoristic name for the 2D open ball of center 0 and radius 1 in Ln norm ).
The equation of the squircle in Ln norm writes  |x|n+|y|n = 1

The attached file gives the exact values of the areas of squircles in norms L2L4L100L1
Unless for n=2 the results are dramatically poor (evalf/Int gives the same wrong results).

The function a(n) gives the exact expression of the squircle area in  Ln norm.

squircle.mw

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