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Another integral

  • Thread starter Stevecgz
  • Start date
  • #1
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[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
 

Answers and Replies

  • #2
James R
Science Advisor
Homework Helper
Gold Member
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Hmm... integration by parts, perhaps?
 
Last edited:
  • #3
TD
Homework Helper
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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]
 
  • #4
68
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Thanks TD, got it worked out now.

Steve
 
  • #5
TD
Homework Helper
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Good :smile:
 

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