### Home > APCALC > Chapter 8 > Lesson 8.4.1 > Problem8-139

8-139.

Express the arc length of each of the following curves as an integral, then evaluate:

1. $f (x) = e^x$, from $x = -2$ to $x = 2$

2. $f (x) = \ln(x)$, from $x = 1$ to $x = e$

Arc length

If $f$ is differentiable on $[a, b]$, then the distance along the curve from $x = a$ to $x = b$ is given by the integral:

$\int _a ^b \sqrt{1+(f^\prime(x))^2}dx$