Math Help - Arc Length Problem, check my answer?

1. [SOLVED] Arc Length Problem, check my answer?

Mind checking my solution anyone? I worry that I may have left out a step because the given coordinates include both x and y values.

3. Re: Arc Length Problem, check my answer?

My bad! Both are in the attachment.

4. Re: Arc Length Problem, check my answer?

Your derivative is incorrect. If \displaystyle \begin{align*} y = \frac{x^4 + 3}{6x} \end{align*}, this simplifies to \displaystyle \begin{align*} y = \frac{1}{6}x^3 + \frac{1}{2}x^{-1} \end{align*}, not \displaystyle \begin{align*} \frac{1}{6x^3} + \frac{1}{2}x^{-1} \end{align*}...

5. Re: Arc Length Problem, check my answer?

That aside, did I use the relationship properly when I just plugged in the x values from the coordinates provided for the definite integral?

6. Re: Arc Length Problem, check my answer?

Your logic seems correct. Now you need to fix the mistake, solve the integral and evaluate the price.