Answer
$$12$$
Work Step by Step
The arc length can be computed as: $L=\int_a^b \sqrt {1+(y^{\prime})^2} \ dx $
We are given that: $y=(4-x^{2/3})^{3/2}$ and $y^{\prime}=-\dfrac{(4-x^{2/3})^{1/2}}{x^{1/3}}$
Now, the arc length is: $L=\int_{0}^{8} 1+(-\dfrac{(4-x^{2/3})^{1/2}}{x^{1/3}})^2 \ dx \\=\int_0^8 \sqrt {\dfrac{4}{x^{2/3}}}\ dx \\=[3 x^{2/3}]_0^8 \\=3[8^{2/3}-0]\\= (3)(4)\\=12$
