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Homework Help: Series accuracy

  1. May 5, 2010 #1
    Ok it says I am to computer using a series accurate to within 0.001.
    gif.latex?\int_{0}^{1}x^2e^{-x^2}.gif

    I'm really not sure where to start. Do I integrate this first by parts? Or am I thinking about this too much? Could someone point me in the right direction please! Help would be much appreciated!
     
  2. jcsd
  3. May 5, 2010 #2

    Mark44

    Staff: Mentor

    The key word is series here. Get the Maclaurin series for e-x2, and then multiply it by x2. Does that give you a place to start?
     
  4. May 5, 2010 #3
    Ok let me just make sure I'm on the right track..

    34zkmzb.jpg

    Is this correct to say?

    sorry, my latex skills are bad.
     
  5. May 5, 2010 #4

    Mark44

    Staff: Mentor

    No, write the series in expanded form, not in closed form. Notice that because you have an alternating series, the error is less in absolute value than your first unused term.

    Your LaTeX looks pretty good!
     
  6. May 5, 2010 #5
    Hmm I'm not exactly sure what to do with this still. How do I integrate an expanded form of a series?
     
  7. May 5, 2010 #6

    Mark44

    Staff: Mentor

    Term by term. This series converges pretty quickly, so you shouldn't need a whole lot of terms.
     
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