# Thread: test question (parametric equation)

1. ## test question (parametric equation)

Find the exact length of the curve.

x=e^t+e^-t y=5-2t 0<t<3

I can simplify the problem to root((e^2t-e^-2t)+2)dt but I'm unsure how the heck I go beyond that point.

2. ## Re: test question (parametric equation)

Originally Posted by some_nerdy_guy
Find the exact length of the curve.

x=e^t+e^-t y=5-2t 0<t<3

I can simplify the problem to root((e^2t-e^-2t)+2)dt but I'm unsure how the heck I go beyond that point.
$\int\limits_{0}^{3}\sqrt{\left(\frac{dx}{dt}\right )^2+\left(\frac{dy}{dt}\right)^2}\, dt = \int\limits_{0}^{3}\sqrt{(e^t-e^{-t})^2+4}\, dt =$

$= \int\limits_{0}^{3} \sqrt{e^{2t}-2+e^{-2t}+4} \,dt= \int\limits_{0}^{3} \sqrt{(e^t+e^{-t})^2} \, dt=\int\limits_{0}^{3} (e^t+e^{-t}) \, dt$