### Home > APCALC > Chapter 10 > Lesson 10.1.3 > Problem10-32

10-32.

Calculate the arc length of the curve $x^{2/3} + y^{2/3} = 1$.

The general formula for arc length is:

$\int_{a}^{b}\sqrt{1+(f'(x))^2}dx$

Rewrite the original equation in y = form.

$y=(1-x^{2/3})^{3/2}$

$y^\prime=\frac{3}{2}(1-x^{2/3})^{1/2}\big(-\frac{2}{3}x^{-1/3}\big)$

Before computing the arclength, graph this curve to determine the bounds of integration and use the symmetry of the graph.

$4\int_0^1\sqrt{1+\frac{9}{4}(1-x^{2/3})\frac{4}{9}x^{-2/3}}$