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Math Help - test question (parametric equation)

  1. #1
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    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.
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  2. #2
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    Crna Gora
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    Re: test question (parametric equation)

    Quote Originally Posted by some_nerdy_guy View Post
    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
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