Integration involving a square root function.

[NewtonianAlch]

Homework Statement

Integrate:

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

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.

 

[algebrat]

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.

 

[NewtonianAlch]

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.

 

[NewtonianAlch]

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.