Mathematics

Problem

Rank the lengths of the following three curves on

[0,1]

from greatest to least: I.

y=x^{3}

II.

y=x^{2}

III.

y=\dfrac{1}{2}x

\text{III} > \text{II} > \text{I}

\text{I} > \text{III} > \text{II}

\text{I} > \text{II} > \text{III}

\text{II} > \text{I} > \text{III}