Arc Length Question

  • #1

Homework Statement



Find the exact length of the curve x=e^t + e^-t , y=5-2t , 0≤ x≤ 3

Homework Equations



∫ √ ( (dx/dt)² + (dy/dt)² )dt

The Attempt at a Solution



My attempt at the solution is hopefully in the attachment. I could use Simpson's and get an approximate length but the directions say to find exact length. So did I mess up my algebra somewhere; I doubt it because this is one of several attempts and I keep getting stuck here. So does anyone know how to get me unstuck? Maybe a trick to make it more integrable? Sorry if I'm missing an obvious step that I can take, but as of now I don't see it. Thanks in advance for the help.
 

Attachments

  • Arc Length .pdf
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Answers and Replies

  • #2
jhae2.718
Gold Member
1,161
20
These problems are often contrived so that you should be able to manipulate the terms under the square root into a perfect square.

Check your expansion of [tex]\left(e^t-e^{-t}\right)^2[/tex].
 
  • #3
Check your expansion of [tex]\left(e^t-e^{-t}\right)^2[/tex].

Yep that was it; my expansion was wrong. Thanks for the help :)
 
  • #4
jhae2.718
Gold Member
1,161
20
No problem. :)
 

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