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Evaluate the integral

  1. Sep 13, 2007 #1
    1. The problem statement, all variables and given/known data

    [tex]\int sin^3(x)cos^2(x)dx[/tex]

    3. The attempt at a solution

    [tex]\int sin^3x(1-sin^2x)dx =[/tex] [tex]\int sin^3x- sin^5xdx[/tex]

    i get stuck here what do i do next and is this even right
     
  2. jcsd
  3. Sep 13, 2007 #2
    we could use complex numbers (de moivres theorem) here and express sin^5x, sin^3x in terms of sin5x, sin3x

    (directly integratable)
     
  4. Sep 13, 2007 #3
    is that from calc 2?
     
  5. Sep 13, 2007 #4

    dextercioby

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    HINT

    [tex] \int \left(1-\cos^{2}x\right) \cos^{2}x \left(\sin x \ dx\right) [/tex]

    Do you know how to use the substitution method ?
     
  6. Sep 13, 2007 #5
    yes i do know how to use substution
     
  7. Sep 13, 2007 #6

    dextercioby

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    Do you see a possible substitution in what i wrote ?
     
  8. Sep 13, 2007 #7
    u = cos x -du = sin x dx right?
     
    Last edited: Sep 13, 2007
  9. Sep 13, 2007 #8

    dextercioby

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    Okay. Very good. Now use it.
     
  10. Sep 13, 2007 #9
    -[tex]\int (u^2 - u^4)du = [/tex] -u^3/3 + u^5/5 +c = -cos^3x/3 + cos^5x/5 + c
     
  11. Sep 13, 2007 #10

    dextercioby

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    Well done.
     
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