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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

    LeonhardEuler

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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

    arildno

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    Just a minor correction.
    We should have:
    [tex]\int\sqrt{C^{2}x^{2}-x^{4}}dx=\int|x|\sqrt{C^{2}-x^{2}}dx[/tex]
     
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