Solving Integral: $\int_{1}^{9} \frac{3x-2}{\sqrt{x}}dx = 44$

[mothership]

$$\begin{equation*} \begin{split} \int_{1}^{9} \frac{3x-2}{\sqrt{x}}dx &= \int_{1}^{9}\frac{3x}{x^{\frac{1}{2}}}dx - \int_{1}^{9}\frac{2}{x^{\frac{1}{2}}}dx \\ \\ &= 3\int_{1}^{9}x^{\frac{1}{2}}dx - 2\int_{1}^{9}x^{\frac{-1}{2}}dx \\ \\ &= 3 \left[ \frac{2}{3}(x^{\frac{3}{2}}) \right]_{1}^{9} - 2 \left[ 2x^{\frac{1}{2}} \right]_{1}^{9} \\ \\ &= 2 \left[9^{\frac{3}{2}} - 1 \right] - 4 \left[ 9^{\frac{1}{2}} - 1 \right] \\ \\ &= 2 \left[27 - 1 \right] - 4 \left[ 3 - 1 \right] \\ \\ &= 2*26 - 4*2 \\ \\ &= 44 \\ \end{split} \end{equation*}$$

 

[dextercioby]

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

Daniel.

 

[arildno]

Hopefully, Josh will agree with Daniel on this issue.