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Integration problem 1

  1. Feb 20, 2013 #1
    1. The problem statement, all variables and given/known data
    [itex]\int_{4}^{9} (\sqrt{x} + \frac{1}{\sqrt{x}})^{2} \textrm{ } dx[/itex]


    2. Relevant equations



    3. The attempt at a solution
    [itex]\int_{4}^{9} (\sqrt{x} + \frac{1}{\sqrt{x}})^{2} \textrm{ } dx \\\\
    \int_{4}^{9} (x + 1 + 1 + \frac{1}{x}) \textrm{ } dx \\\\
    \frac{x^2}{2} + 2x + ln(x) | \textrm{4 to 9} \\\\
    (27 + ln(9)) - (\frac{88}{9} + ln(4)) \\\\
    \frac{155}{9} + ln(\frac{9}{4})[/itex]

    The solution says this is incorrect...can anyone correct me where I integrated wrong?
     
  2. jcsd
  3. Feb 20, 2013 #2
    I think you just goofed up when plugging in 9 and 4. Everything up until that point is correct.
     
  4. Feb 20, 2013 #3

    Mark44

    Staff: Mentor

    Your integration was fine. You have a mistake when you evaluate your antiderivative, when x = 4. If x = 4, x2/2 = 16/2, not 88/9.
     
  5. Feb 20, 2013 #4

    Zondrina

    User Avatar
    Homework Helper

    ##9^2 ≠ 27##

    In specific : x^2/2 = 81/2
     
    Last edited: Feb 20, 2013
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