Josh, is this correct?

  • Thread starter mothership
  • Start date
  • #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]
 

Answers and Replies

  • #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.
 
  • #3
arildno
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Hopefully, Josh will agree with Daniel on this issue.
 

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