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Indefinite Trignometric Integral

  1. Feb 6, 2016 #1
    1. The problem statement, all variables and given/known data
    ∫sinxcos(x/2)dx

    This isn't an actual homework problem, but one I found that I'm working on for test prep.

    2. Relevant equations


    3. The attempt at a solution

    ∫sinxcos(x/2) dx = ∫sinx√((1+cosx)/2) dx

    u = ½ + ½ cosx
    -2 du = sinx dx

    -2∫√(u) du = -2(2/3⋅u3/2) + c

    -2(2/3⋅u3/2) + c = -4/3⋅[(1+cosx)/2)3/2] + c
    -4/3⋅[(1+cosx)/2)3/2] = -4/3⋅(cos(x/2))3/2 + c

    I tried to check my solution by graphing my answer with theirs, but the table is displaying different values.
     
    Last edited: Feb 6, 2016
  2. jcsd
  3. Feb 6, 2016 #2

    Samy_A

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    You have an error in the last line:
    The formula you used for the substitution is ##\sqrt{\frac{1+\cos x}{2}}=\cos \frac{x}{2}##
     
  4. Feb 6, 2016 #3
    Gotcha, so it's probably easier to leave it where I had it in the second line. For some reason the solution isn't working, still. Even when I just plug the integral on my graphic calculator. :/

    Is there a trick to getting my square roots to look fancy like yours so I can clean it up when I post?
     
  5. Feb 6, 2016 #4
    Theres another way, I think it is easier. Remember the product to sum trigonometric identities? Use it!
     
  6. Feb 7, 2016 #5

    Samy_A

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    Weird, I get the same result as you, except for the erroneous square root in the final result.

    @MidgetDwarf 's suggestion is also good, but as said, you really are one symbol away from the solution.

    Yes, I use ##\LaTeX##. It may look difficult if you never used it, but you'll learn it quickly. It makes posts with equations much more readable, and I highly recommend the use of it.

    There is a guide here, there is also a link to that guide in the bottom left of the edit box.
    If you see a complex ##\LaTeX## expression and want to see how it was composed, right-click the expression written in it and select "Show Math As -> TeX Commands". A small window will appear containing the code used for that expression. Or just quote a post: the ##\LaTeX## code will in general appear between ## or $$ tags.
     
    Last edited: Feb 7, 2016
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