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.