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!

Homework Help: Integration involving a square root function.

  1. Jun 4, 2012 #1
    1. The problem statement, all variables and given/known data

    sqrt(1/4 + t^2 + t^4)

    3. The attempt at a solution

    I'm really not sure on how to go about integrating this, it's actually integrate from -1 to 1, the solutions manual has a method I'm not familiar with. I thought of factorising it first, although doing that hasn't made it any easier.
  2. jcsd
  3. Jun 4, 2012 #2
    I stared at it blankly for a little bit. But then I asked wolfram for the steps and said aha, why didn't I see that. If you pull the 1/4 out, you should recognize that 4t^4+4t^2+1 is the square of 2t^2+1. So you are integrating |2t^2+1|/2. But the absolute value goes away since 2t^2+1 is never negative.
  4. Jun 4, 2012 #3
    I saw that in Wolfram too, although I didn't quite understand what was happening there.

    So are you saying that pulling out the 1/4 from a square root doubles it when you pull it out? Or any other number for that matter.
  5. Jun 4, 2012 #4
    Hmm, I think I see what you mean now, since the root of 1/4 is 0.5 you can take that out.

    Interesting, doubt I'd have figured out all that myself without some help, thanks.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook