1. The problem statement, all variables and given/known data Hello, I have an arc length problem that I’m stuck on, and I would really appreciate it if someone could help me out. I understand the arc length formula and everything, it’s evaluating the integral produced by it. The author in the book I got this problem from tells the reader that arc length problems can produce tricky integrals, and therefore he shouldn’t have to show the work involved (real helpful). Anyway, the entire problem is irrelevant, so I’m just going to list the part that I don’t understand. Sorry for the crazy notation, but I couldn’t figure out how to do math symbols on the computer. I'm supposed to find the arc length along f(x)=x^(2/3) from x=8 to x=27. The first step listed starts out after everything has been plugged into the formula. 27 INTEGRAL * square root(1+(4/9)x^(-2/3))dx 8 27 = (1/3) INTEGRAL * square root(9+4x^(-2/3))dx 8 27 =(1/3) INTEGRAL*x^(-1/3)* square root(9x^(2/3)+4)dx 8 I understand the first step, but the author completely lost me on steps two and three. If I could find out what happened in those two steps, I would understand the whole problem. I don’t need anything else explained after the third step, because it involves using u-substitution, which I understand fairly well. 2. Relevant equations The formula for arc length is: B Arc length= INTEGRAL* square root(1+(f ‘(x))^2) dx A 3. The attempt at a solution When I first attempted the problem, I didn’t think the integral looked all that difficult. I thought that I could simply take the square root away by raising the inside term to the power of ½ and integrating. But apparently it’s much more subtle than that. I would really appreciate some guidance with this. I hope the notation I used wasn’t confusing, and I can clarify it if anyone wants me to.