# What is the arclength of #(t-3,t+4)# on #t in [2,4]#?

##### 1 Answer

Apr 2, 2018

#### Explanation:

The formula for parametric arc length is:

We begin by finding the two derivatives:

This gives that the arc length is:

In fact, since the parametric function is so simple (it is a straight line), we don't even need the integral formula. If we plot the function in a graph, we can just use the regular distance formula:

This gives us the same result as the integral, showing that either method works, although in this case, I'd recommend the graphical method because it is simpler.