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Another integral

  1. Sep 25, 2005 #1
    [tex]\int (4-x)\sqrt{4x-x^2}dx[/tex]

    I'm uncertain how to find this integral, or even how to start it. Any guidence would be appreciated. Thanks.

    Steve
     
  2. jcsd
  3. Sep 25, 2005 #2

    James R

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    Hmm... integration by parts, perhaps?
     
    Last edited: Sep 25, 2005
  4. Sep 26, 2005 #3

    TD

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    It would be a lot easier if the integral were

    [tex]\int {\left( {4 - 2x} \right)\sqrt {4x - x^2 } dx} [/tex].

    If not, you'll need integration by parts indeed and I suspect you'll be getting an arcsin too :smile:

    Think about

    [tex]\sqrt {4x - x^2 } = \sqrt {4 - \left( {x - 2} \right)^2 } = 2\sqrt {1 - \left( {\frac{{x - 2}}
    {2}} \right)^2 } [/tex]
     
  5. Sep 27, 2005 #4
    Thanks TD, got it worked out now.

    Steve
     
  6. Sep 27, 2005 #5

    TD

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    Good :smile:
     
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