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Integration Problem

  1. Nov 13, 2006 #1
    Could someone plz help me integrate (sin x)^3. Can i use any simpler method asides from integration by parts.??
     
  2. jcsd
  3. Nov 13, 2006 #2
    [tex] \int \sin^{3} x \; dx = \int (1-\cos^{2}x)\sin x \; dx [/tex].

    Let [tex] u = \cos x [/tex]
     
  4. Nov 13, 2006 #3

    HallsofIvy

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    Why do we have so many people who think differentiation and integeration are pre-calculus?
     
  5. Nov 13, 2006 #4
    yeh its kind of the crux of calc rly
     
  6. Nov 14, 2006 #5

    VietDao29

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    Homework Helper

    Generally, when the power of the sine function is odd, we use the substitution u = cos(x), and change all sine functions to cosine functions by using the Pythagorean Identity : sin2x + cos2x = 1.
    When the power of the cosine function is odd, we use the substitution u = sin(x), and change all cosine functions to sine functions by using the Pythagorean Identity : sin2x + cos2x = 1.
    When both powers are even, we use the Power-Reduction Formulae. :)
    And in your problem, the power of sine is odd, hence, we use the substitution: u = cos(x)
     
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