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Integrate sqrt(1+4x^2)

  1. Jan 21, 2014 #1
    1. The problem statement, all variables and given/known data

    Integrate sqrt(1+4x^2)

    limits x = 0 to x = 1

    2. Relevant equations



    3. The attempt at a solution

    let 2x = sinhu

    I = 0.5 ∫ (coshu)^2du

    limits u = 0 u = sinh^-1(2)

    0.5 ∫ (e^2u +e^-2u +2)/4 du

    0.5 [(e^2u)/8 -(e^-2u)/8 +2u]

    I = 2.56 which is wrong :(

    why is it wrong?

    please help!
     
    Last edited: Jan 21, 2014
  2. jcsd
  3. Jan 21, 2014 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Well, for one thing 0.5 ∫ (e^2u +e^-2u +2)/4 du becomes
    0.5 [(e^2u)/8 -(e^-2u)/8 +u/2]. Did you forget to divide the last term by 4?
     
  4. Jan 21, 2014 #3
    You started out well. I think you made an arithmetic mistake when you multiplied your expression through by .5 -- you got ##e^{2u}/8 + e^{-2u}/8 +2u##. Where did you get 2u. Shouldn't it be u/4?
     
  5. Jan 23, 2014 #4
    what a silly mistake, i feel embarrassed :S
     
  6. Jan 23, 2014 #5
    I recently wrote that 25 is divisible by 3. And just a few months ago based a proof on the non-fact that 10 is prime. Talk about embarrassed. Losing a factor of 4 is much more understandable.

    We cannot escape these boneheaded errors.
     
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