Sure

For the first one

$\displaystyle y = x^{\frac{1}{2}} - \frac{1}{3}x^{\frac{3}{2}}$

$\displaystyle y' = \frac{1}{2}x^{-\frac{1}{2}} - \frac{1}{2}x^{\frac{1}{2}}$

$\displaystyle [y']^{2} = \frac{1}{4}x^{-1} - \frac{1}{2} + \frac{1}{4}x$

$\displaystyle s = \int^{4}_{1} \sqrt{\frac{1}{4}x^{-1} + \frac{1}{2} + \frac{1}{4}x} \, \, dx$

and this is where I get stuck, although I'm sure I'm missing something obvious. I tried pulling out the quarter and messing with it a bit like that. But at the end of the day it's those powers of

*x* which are confusing me