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Math Help - cal 2

  1. #1
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    cal 2

    evaluate the limits of pie and 0 (x+sinnx)dx
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  2. #2
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    Quote Originally Posted by lay137 View Post
    evaluate the limits of pie and 0 (x+sinnx)dx
    What are you trying to find? The Fourier Series?

    We need to find, (assume n>1)
    \int_0^{\pi} (x+\sin nx )dx
    By linearity,
    \frac{1}{2}x^2-\frac{1}{n}\cos nx\big|^{\pi}_0
    \frac{1}{2}\pi^2-\frac{1}{n}\cos \pi n+\frac{1}{2}
    If n is even, then we have,
    \frac{1}{2}\pi^2 - \frac{1}{2}+\frac{1}{2}=\frac{1}{2}\pi^2.
    If n is odd, then we have,
    \frac{1}{2}\pi^2+\frac{1}{2}+\frac{1}{2}=\frac{1}{  2}\pi^2+1
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  3. #3
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    Quote Originally Posted by lay137 View Post
    evaluate the limits of pie and 0 (x+sinnx)dx
    And, just as a note, the Greek letter \pi is "pi", not "pie!"

    -Dan
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