Answer
3.4467
Work Step by Step
The formula for the arc length of a curve on the interval (a,b) is $_{a}\int^{b}(\sqrt {1+(dy/dx)^2}$. The derivative of the function $x-ln(x)$ with respect to x is: $1-1/x$. Plugging this in, we get: $_{1}\int^{4}(\sqrt {1+(1-1/x)^2}$. A calculator gives the final answer: 3.4467.
