1. The problem statement, all variables and given/known data Find the arclength of the parametrized path x(t) = (t^2)/2 , y(t) = (t^3)/3 for 1<t<3. 2. Relevant equations Arc Length Formula 3. The attempt at a solution x'=t and y'=t^2. Putting them into the arc length formula, I get sqrt(t^2 + t^4) inside. I'm confused about how to simplify this part. The answer (10sqrt(10)-2sqrt(2))/3 suggests the quadratic formula somewhere along the way. I could probably pull out a variable into sqrt(t^2(t^2 + 1)) or tsqrt(t^2+1) but how do I use the quadratic equation in this case?