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duff44

  • 3 years ago

find the integral of 1/x sqrt(5-x^2) not sure how to do an identity with the 5 in there

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  1. tkhunny
    • 3 years ago
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    What would you do if it were a '1', rather than a '5'?

  2. Goten77
    • 3 years ago
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    |dw:1359690189282:dw| hmm let me think for a sec

  3. duff44
    • 3 years ago
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    well if it was a 1 I could use a^2-x^2 as the identity for sin but I dont think taking sqrt of 5 is the way to go.

  4. tkhunny
    • 3 years ago
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    You didn't quite answer my question. What substitution would you actually use if it were a 1?

  5. matricked
    • 3 years ago
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    assume x=sqrt(5)*sinp ...

  6. duff44
    • 3 years ago
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    I would make x=sin theta so|dw:1359690857236:dw|

  7. tkhunny
    • 3 years ago
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    Perfect. So, \(1 - x^{2}\) leads to \(x = \sin(\theta)\). You already suggested that \(a^{2} - x^{2}\) leads to \(x = a\cdot\sin{\theta}\). Why would \(5 - x^{2}\) lead to anything but \(x = \sqrt{5}\cdot\sin(\theta)\)?

  8. duff44
    • 3 years ago
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    |dw:1359691617818:dw| then just plug back in x for theta?

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