1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Simplifying Square Roots

  1. May 26, 2014 #1
    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?
  2. jcsd
  3. May 26, 2014 #2


    User Avatar
    Science Advisor
    Homework Helper

    You don't use the quadratic equation. You just integrate ##t \sqrt{t^2+1}##. It's not hard, just do it by a substitution.
  4. May 26, 2014 #3
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted