The graph of the equation x^2/3 + y^2/3 = 1 is one of a family of curves called astroids (not “asteroids”) because of their starlike appearance. Find the length of this particular astroid by finding the length of half the first-quadrant portion, y = (1 - x^2/3)^3/2, √2/4 ≤ x ≤ 1, and multiplying by 8.

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X I = {/z^² + ε/zx 0 y