Find the length of the arc of this curve from (−27, 9) to (8, 4).
$$y^3=x^2$$
I know how to use the simple arc length formula to solve a general equation. What's throwing me off about this problem is the specific points given. Do I just pick either the x or the y values to use in the arc length formula? For example, if I choose to use x values to evaluate:
$$\int_{-27}^8 \sqrt{1 + \left(\frac 49\ x\right)^{-2/3}}\,dx $$
Does this setup look correct? I did it this way and have been getting the wrong answer.