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Homework Help: Help with partial fractions

  1. Aug 9, 2010 #1
    1. The problem statement, all variables and given/known data

    Evaluate the integral:

    [tex]\int_{1}^2 \frac{4y^2 - 7y -12}{y(y+2)(y-3)}dy
    [/tex]

    2. Relevant equations

    None.

    3. The attempt at a solution

    [tex]\frac{4y^2 -7y -12}{y(y+2)(y-3)} = \frac{A}{y} + \frac{B}{y+2} + \frac{D}{y-3}[/tex]

    [tex]y = 0: -12 = -6A \rightarrow A=2[/tex]

    [tex]y = -2: 16 + 14 - 12 = 10B[/tex]

    [tex]18 = 10B \rightarrow B = \frac{18}{10} = \frac{9}{5}[/tex]

    [tex]y = 3: 36 - 21 -12 = 15D
    [/tex]

    [tex]3 = 15D \rightarrow D = \frac{3}{15} = \frac{1}{5}[/tex]

    =[tex]\int_{1}^2 \frac{2}{y} + \frac {\frac{9}{5}}{y + 2} + \frac{\frac{1}{5}}{y - 3} dy[/tex]

    =[tex]2ln|y| + 9ln|5y+2| + ln|y - 3| ]_{1}^{2}[/tex]

    [tex]2ln2 + 9ln12 - (9ln7 + ln2)[/tex]

    [tex]ln2 + 9ln12 - 9ln7

    [/tex]

    The correct answer is [tex]\frac {27}{5}ln2 - \frac{9}{5}ln3[/tex] but I cant see what I did wrong.
     
  2. jcsd
  3. Aug 9, 2010 #2

    Mark44

    Staff: Mentor

    The mistakes are above. The 2nd and 3rd terms in your antiderivative are incorrect. I was able to get the same answer as in the book.
     
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