Answer
Total length of arc is 3
Work Step by Step
$y=(1-x^{\frac{2}{3}})^{\frac{3}{2}}$
$L=\int_a^b\sqrt{1+\Big(\frac{dy}{dx}\Big)^2}dx$
$a=0$; $b=1$
$\frac{dy}{dx}=-\frac{\sqrt{1-x^{\frac{2}{3}}}}{x^{\frac{1}{3}}}$
$L=\int_0^1\sqrt{1+\Big(-\frac{\sqrt{1-x^{\frac{2}{3}}}}{x^{\frac{1}{3}}}\Big)^2}dx=\frac{3}{2}$
Total length of arc is 3
