1. Approximate value of integral

Find the length "L" of a certain curve given by L=

- Im having a hard time with this, any help with be very appreciated
-thanks

2. Make the following substitution:
$\displaystyle u = 4+ 3x$
$\displaystyle du = 3dx \: \: \Rightarrow \: \: dx = \frac{du}{3}$

Also, we must change our limits of our integral:
$\displaystyle u(8) = 4 + 3(8) = 28$
$\displaystyle u(2) = 4 + 3(2) = 10$

So substituting all these in:
$\displaystyle = \int_{u(2)}^{u(8)}\! \sqrt{u} \frac{du}{3} \: = \: \frac{1}{3} \int_{10}^{28} u^{\frac{1}{2}}du$

3. Im sorry im very new to integrals, and need to see all the steps involved in solving this problem so I have an idea on what to do on future problems.
-Thank you

4. This is a must-know integral: $\displaystyle \int x^{n} dx = \frac{x^{n+1}}{n+1} + C$ where $\displaystyle n \neq -1$ and is some constant.

Do you not see how that applies to the last integral I gave you?

6. I think i figured this out.. is the correct answer 25.8976?

7. From where we last left off:
$\displaystyle \frac{1}{3} \int_{10}^{28} u^{\frac{1}{2}}du = \frac{1}{3} \cdot \frac{u^{\frac{3}{2}}}{\frac{3}{2}} \bigg|_{10}^{28} \: \: = \: \: \frac{2}{9} u^{\frac{3}{2}} \bigg|_{10}^{28} \: \: = \: \: \frac{2}{9} \left( 28^{\frac{3}{2}} - 10^{\frac{3}{2}} \right) \: \approx \: 25.898$