CPM Homework Help : APCALC Problem 9-11

Calculate the exact length of the curve $y = 2x^{3/2}$ for $0 ≤ x ≤ 5$ . Use a sketch of the graph to check whether your answer is reasonable.

Hint:

The general formula for arc length is:

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

Step 1:

$y'=3x^{1/2}$

Step 2:

$\int_{0}^{5}\sqrt{1+(3x^{1/2})^2}dx=\int_{0}^{5}\sqrt{1+9x}dx$

Step 3:

$=\left.\Big(\frac{1}{9}\Big)\Big(\frac{2}{3}\Big)(1+9x)^{3/2}\right|_0^5$