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Homework Help: Ideas as to how I should start to integrate this one?

  1. Sep 24, 2005 #1
    [tex]\int (C^2x^2-x^4)^{0.5} dx [/tex]

    C is a constant

    any ideas as to how I shoud start to integrate this one?
  2. jcsd
  3. Sep 24, 2005 #2


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    Yeah, just factor out x^2, so you have
    [tex]\int x\sqrt{C^2-x^2}dx[/tex]
    Then just make the substitution [itex]u=x^2[/itex].
  4. Sep 24, 2005 #3
    so then how would I integrate

    [tex]\int (C^2-u)^{0.5}[/tex]
  5. Sep 25, 2005 #4
    You can make another substitution, e.g. [tex]z = C^2 - u [/tex] or just make your original substitution [tex]u = C^2 - x^2 [/tex], which gives

    [tex]du = -2x dx[/tex]

    [tex]\frac{du}{-2x} = dx [/tex]

    then you just use your normal integration rules.
  6. Sep 25, 2005 #5


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    Dearly Missed

    Just a minor correction.
    We should have:
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