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Math Help - I don't know what I did wrong on this integral..

  1. #1
    Member Em Yeu Anh's Avatar
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    Angry I don't know what I did wrong on this integral..

    Question is: Evaluate \int_{25}^{36}\frac{ln(y)}{\sqrt(y)}dy

    Integrating by parts,
    u=ln(y), du=\frac{dy}{y}
    dv=\frac{1}{\sqrt{y}}dy, v = 2\sqrt{y}

    =[2\sqrt{y}ln(y) - 2\int\frac{1}{\sqrt{y}}dy]_{25}^{36}

    = [2\sqrt{y}ln(y) - 4\sqrt{y}]_{25}^{36}

    =(12ln(36)-24) - (10log25-20)

    =12log36-10log25-4

    Strangely this is the same answer that Wolfram Alpha gives, but the decimal value is different. When evaluated on my calculator I'm getting 0.696, the correct answer is 6.813 can someone point out my error? Thanks!
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  2. #2
    Super Member General's Avatar
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    You changed the "ln" to a "log".
    ln=log_{e}
    log=log_{10}
    Big difference.
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  3. #3
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    you are using log when you should be using ln (natural log) yes the base matters.... =) no mistakes with calculus, just logarithms
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  4. #4
    Member Em Yeu Anh's Avatar
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    That's the second time in a row I made that same mistake! Maybe it's my lack of sleep...haha thank you guys!
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