QuestionFind the arc length of the following curve on the given interval. $$y=\frac{1}{3} x^{3 / 2} \text { on }[0,54]$$

Studdy Solution
Calculate the numerical value:
$$(14.5)^{3/2} = \sqrt{14.5^3}$$
Calculate $14.5^3$:
$$14.5^3 = 14.5 \times 14.5 \times 14.5 = 3048.625$$
Then:
$$\sqrt{3048.625} \approx 55.22$$
Thus:
$$L = \frac{8}{3} \left[ 55.22 - 1 \right]$$ $$L = \frac{8}{3} \times 54.22$$ $$L \approx 144.59$$
The arc length of the curve on the interval $[0, 54]$ is approximately:
$$\boxed{144.59}$$