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Evaluating an arc length

  1. Oct 27, 2012 #1
    Hello everyone, I am having a bit of an issue evaluating the arc length of the function 1/2(e^x+e^-x) interval [0,2]. We were instructed to solve using the arc length formula square root of 1+(dy/dx)^2. The solution should be 3.627 according to my CAS. However my calculations are yielding 3.511.


    arc length of the function 1/2(e^x+e^-x) interval [0,2]


    2. Relevant equations


    square root of 1+(dy/dx)^2


    3. The attempt at a solution

    F(x)= 1/2(e^x+e^-x)
    F'(X)= 1/2(e^x-e^-x)
    F'(x)^2= (e^2x - 2 - e^-2x)/4 ==> ((e^2x)/4) - (1/2) - (1/4e^2x)

    So I try to evaluate the integral from the interval [0,2] of the square root of 1+[(e^2x)/4 - (1/2) - (1/4e^2x)] and end up with 3.511.

    any help is greatly appreciated. Thank you in advance
     
  2. jcsd
  3. Oct 27, 2012 #2

    haruspex

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    Check the signs.
     
  4. Oct 27, 2012 #3
    such a silly mistake.. it has been a long day. Thank you much
     
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