For , let be the graph of on the interval . If the length of on this interval is…

MATHEMATICS · Subjective · AP · Calculus BC · Applications of Integration · Applications of Integration

Problem

For

k>0

, let

C_k

be the graph of

y = \dfrac{x^{3}}{k}

on the interval

0 \le x \le 1

. If the length of

C_k

on this interval is

2

units, determine

k

, correct to the nearest hundredth.