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Math Help - tricky integration of a fraction

  1. #1
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    tricky integration of a fraction

     <br />
\int \frac{200000}{20000P - P^2} dP<br />

    i am so confused as to what to do, someone please help!!
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  2. #2
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    Quote Originally Posted by wik_chick88 View Post
     <br />
\int \frac{200000}{20000P - P^2} dP<br />

    i am so confused as to what to do, someone please help!!
    Use the method of partial fraction decomposition.
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  3. #3
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    this is what i have:
    \frac{1}{P(20000-P)} = \frac{A}{P} + \frac{B}{20000-P} (i brought the 200000 out the front of the integral)
    = \frac{20000A - AP + BP}{P(20000-P)}
    = \frac{20000A + (B-A)P}{20000-P}

    equate coefficients:
    20000A = 1, therefore A = \frac{1}{20000}
    B - A = 0, therefore B = A = \frac{1}{20000}

    therefore:
    \frac{1}{P(20000-P)} = \frac{1}{20000P} + \frac{1}{20000(20000-P)}

    have i gotten it right so far? i know where to go from here, as long as i havent made any mistakes!!
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  4. #4
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    Quote Originally Posted by wik_chick88 View Post
    this is what i have:
    \frac{1}{P(20000-P)} = \frac{A}{P} + \frac{B}{20000-P} (i brought the 200000 out the front of the integral)
    = \frac{20000A - AP + BP}{P(20000-P)}
    = \frac{20000A + (B-A)P}{20000-P}

    equate coefficients:
    20000A = 1, therefore A = \frac{1}{20000}
    B - A = 0, therefore B = A = \frac{1}{20000}

    therefore:
    \frac{1}{P(20000-P)} = \frac{1}{20000P} + \frac{1}{20000(20000-P)}

    have i gotten it right so far? i know where to go from here, as long as i havent made any mistakes!!
    Correct.
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  5. #5
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    It is correct, math tags?
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  6. #6
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    oops forgot to wrap the text!

    this is what i have:
    \frac{1}{P(20000-P)} = \frac{A}{P} + \frac{B}{20000-P} (i brought the 200000 out the front of the integral)
    = \frac{20000A - AP + BP}{P(20000-P)}
    = \frac{20000A + (B-A)P}{P(20000-P)}
    equate coefficients:
    20000A = 1, therefore A = \frac{1}{20000}
    B - A = 0, therefore B = A = \frac{1}{20000}

    therefore:
     <br />
\frac{1}{P(20000-P)} = \frac{1}{20000P} + \frac{1}{20000(20000-P)}<br />
    have i gotten it right so far? i know where to go from here, as long as i havent made any mistakes!!
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