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Josh, is this correct?

  1. May 7, 2005 #1
    [tex]
    \begin{equation*}
    \begin{split}
    \int_{1}^{9} \frac{3x-2}{\sqrt{x}}dx &= \int_{1}^{9}\frac{3x}{x^{\frac{1}{2}}}dx - \int_{1}^{9}\frac{2}{x^{\frac{1}{2}}}dx \\ \\
    &= 3\int_{1}^{9}x^{\frac{1}{2}}dx - 2\int_{1}^{9}x^{\frac{-1}{2}}dx \\ \\
    &= 3 \left[ \frac{2}{3}(x^{\frac{3}{2}}) \right]_{1}^{9} - 2 \left[ 2x^{\frac{1}{2}} \right]_{1}^{9} \\ \\
    &= 2 \left[9^{\frac{3}{2}} - 1 \right] - 4 \left[ 9^{\frac{1}{2}} - 1 \right] \\ \\
    &= 2 \left[27 - 1 \right] - 4 \left[ 3 - 1 \right] \\ \\
    &= 2*26 - 4*2 \\ \\
    &= 44 \\
    \end{split}
    \end{equation*}
    [/tex]
     
  2. jcsd
  3. May 7, 2005 #2

    dextercioby

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    I dunno who Josh is and,in case you haven't figured out yourself yet,the solution you found is perfect...

    Daniel.
     
  4. May 7, 2005 #3

    arildno

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    Dearly Missed

    Hopefully, Josh will agree with Daniel on this issue.
     
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