# What is the arc length of #f(x) = x-xe^(x^2) # on #x in [ 2,4] #?

##### 1 Answer

Jan 1, 2018

#### Explanation:

The formula for arc length of

First we'll work out the derivative of our function:

To figure out the second part, we'll use the product rule:

In our case, we get:

We can use the chain rule, which says:

This gives us:

If we then plug this into our formula, we get:

This integral doesn't have an elementary answer that I've been able to find, but the value can be approximated to be roughly