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Takehome Test Check

  1. Sep 20, 2007 #1
    [SOLVED] Takehome Test Check

    Have a take home test that is due tomorrow at noon. Got 3 of the 4 done and I thought that it would be a good idea to have better mathematicians then myself check it for me. So, if anybody feels like doing the work;

    1. Integration by Parts

    [tex]\int\sin(log_{2}x)dx[/tex]

    [tex]u = \sin(log_{2}x)[/tex]

    [tex]du = \frac{\cos(log_{2}x)}{xlog2}dx[/tex]

    dv = dx, v = x

    [tex]x\sin(log_{2}x)-\int\frac{x\cos(log_{2}x)}{xlog2}[/tex]

    [tex]x\sin(log_{2}x)-\frac{1}{log2}\int\cos(log_{2}x)dx[/tex]

    Then do it again.

    [tex]u = \cos(log_{2}x)[/tex]

    [tex]du = \frac{-\sin(log_{2}x)}{xlog2}dx[/tex]

    dv = dx, v = x

    [tex]x\cos(log_{2}x)+\int\frac{x\sin(log_{2}x)}{xlog2}[/tex]

    [tex]x\cos(log_{2}x)+\frac{1}{log2}\int\sin(log_{2}x)dx[/tex]

    Now put it all together.

    [tex]x\sin(log_{2}x)-\frac{1}{log2}(x\cos(log_{2}x)+\frac{1}{log2}\int\sin(log_{2}x)dx)=\int\sin(log_{2}x)dx[/tex]

    [tex]x\sin(log_{2}x)-\frac{1}{log2}x\cos(log_{2}x)=\frac{log^{2}2+1}{log^{2}2}\int\sin(log_{2}x)dx[/tex]

    Answer:

    [tex]\frac{log^{2}2(\sin(log_{2}x)-\frac{1}{log2}x\cos(log_{2}x))}{log^{2}2+1}=\int\sin(log_{2}x)dx[/tex]
     
    Last edited: Sep 20, 2007
  2. jcsd
  3. Sep 20, 2007 #2

    Dick

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    You were doing fine until you tried to "put it all together". Then there's some algebraic slip ups. Try it again. E.g. I get (log2)^2+1 in the denominator.
     
  4. Sep 20, 2007 #3
    Ah, yea, slight of...latex? Just got impatient while painstakingly going through the code. 1/Log2 * 1/log2 = 1/(log2)^2......(log2)^2/(log2)^2 - 1/(log2)^2 = (log2)^2-1 / (log2)^2 and from there multiply both sides by denom then devide both sides by num.

    Correct now?
     
  5. Sep 20, 2007 #4

    Dick

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    That looks familiar - but don't you get ((log2)^2+1)/(log2)^2??? In 'putting it all together' you have a sign error on integral(sin) on the LHS.
     
  6. Sep 20, 2007 #5
    Edited the original post. How's that?
     
  7. Sep 20, 2007 #6

    Dick

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    I don't see any change. Did the TeX not regenerate?
     
  8. Sep 20, 2007 #7
    Got to push refresh button.
     
  9. Sep 20, 2007 #8

    Dick

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    Ok, got it. You left out an 'x' in the sin term, but that's just a typo.
     
  10. Sep 20, 2007 #9
    Thanks again =P
     
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