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Solving Integrals Using a Known Mac Series (Sin(x))

  1. Feb 24, 2009 #1
    1. The problem statement, all variables and given/known data
    Assume that sin(x) equals its Maclaurin series for all x. Use the Maclaurin series for sin(7x^2) to evaluate the integral https://webwork.math.lsu.edu/webwork2_files/tmp/equations/f4/767c0643696d085d77f9a697294a311.png

    Your answer will be an infinite series. Use the first two terms to estimate its value.

    2. Relevant equations
    Inline44.gif


    3. The attempt at a solution
    http://img27.imageshack.us/img27/5028/mathhelp2k.jpg [Broken]

    After the final step in the picture, I plugged in n=0 and 1 to get my 0th and 1st terms, then I added them together and I got: 0.754110411. This is wrong, however.. can someone please help me diagnose this problem?
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Feb 24, 2009 #2
    You forgot powering the 7, you need 7^(2n+1).
     
  4. Feb 24, 2009 #3
    Thank you, I see my error now and the suggestion lead me to a correct answer.
     
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