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Math Help - Length of curve

  1. #1
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    Length of curve

    I'm getting stuck doing my integration for the following problem:

    Find the length of the curve r(t) = ((2)^(1/2)t)i + (e^t)j + (e^-t)k

    Sorry I'm not quite sure how to use the notation on this site yet but that first term is supposed to be a root 2 multiplied by t.
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  2. #2
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    Quote Originally Posted by Todeezy View Post
    I'm getting stuck doing my integration for the following problem:

    Find the length of the curve r(t) = ((2)^(1/2)t)i + (e^t)j + (e^-t)k

    Sorry I'm not quite sure how to use the notation on this site yet but that first term is supposed to be a root 2 multiplied by t.
    The derivative of the vector function is \sqrt{2}\vec{i}+ e^t\vec{j}- e^{-t}\vec{k} and its length is \sqrt{2+ e^{2t}+ e^{-2t}}. If you look closely at the terms inside the square root, you will see that they are e^{2t}+ 2+ e^{-2t}= (e^{t})^2+ 2e^{t}e^{-t}+ (e^{-t})^2 = (e^t+ e^{-t})^2. That makes the integral very easy!
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