$$ 80=\int_0^b \sqrt{1+f'(x)^2}dx $$ ($b$ is a nonzero constant)
Context: I was trying to do the amazon cable question (my friend sent it to me, I know the answer is zero, but I wanted to know how to do this still), and I tried using the arc length integral formula to figure out more about $f(x)$ (which I set to be the graph of the cable between the posts). The problem gives the length of the cable, and so this question arose.