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Homework Help: Series approx of and integral

  1. Aug 31, 2010 #1
    I need help solving the following (it is due tomorrow :frown: and it just got assigned yesterday ):

    use series methods to obtain the approximate value of integral(from 0 to1) of (1-e^x)/x dx

    What I have thought of so far is to use the Taylor series approx for e^x and carry that out to a few terms then solve for 1 and 0 and plug it into the original equation but I'm not sure that I'm headed in the right direction. I took a year off from school and now I'm having to relearn a bunch of things that were once simple but now seem quite challenging. Any help is appreciated. Thanks.
     
    Last edited: Aug 31, 2010
  2. jcsd
  3. Aug 31, 2010 #2

    hunt_mat

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    Looks good to me. You should get an easy power series to integrate and then you just substitute in 1 and 0.

    Mat
     
  4. Aug 31, 2010 #3
    I plugged in the Taylor series for e^x and took that out to 6 terms then integrated it from 0 to 1 and got 1.262.....does that sound about right?
     
  5. Aug 31, 2010 #4

    Office_Shredder

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    The integrand is negative so you should end up with a negative answer.

    As an example just using two terms, ex=1+x you would end up with

    [tex]\int_0^1 \frac{1-(1+x)}{x}dx = \int_0^1 \frac{-x}{x}dx=-1[/tex]

    As you add more terms the integral should become more negative
     
  6. Aug 31, 2010 #5
    Thanks for pointing that out Office Shredder. There was a negative that I had forgotten to carry over. So I got -1.262 with 6 terms in the e^x Taylor series.
     
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