Given $\displaystyle y=f(x)$ the formula for arc length $\displaystyle L$ over the interval $\displaystyle [a,b]$:

$\displaystyle L = \int_a^b \sqrt{1+[f'(x)]^2} dx$

or $\displaystyle \int_a^b \sqrt{1+(\frac{dy}{dx})^2}dx $

With the formula above find the arc length of the following functions over the given interval.

1. $\displaystyle y=1+6x^{3/2}, [0,1]$

Answer: $\displaystyle \frac{2}{243}(82\sqrt{82}-1)$

2. $\displaystyle y=\frac{x^5}{6}+\frac{1}{10x^3}, [1,2]$

Answer: $\displaystyle \frac{1261}{240}$

I found the derivatives of the functions, $\displaystyle 9\sqrt{x}$ and $\displaystyle \frac{5x^4}{6}-\frac{3}{10x^4}$, respectively, and plugged them in, simplified, substituted and converted limits if I had to, but still don't get the correct answer. Could someone tell me what I'm doing wrong?