Find the arc length of a curve over an interval

[bocobuff]

Homework Statement

I'm trying to find the arc length of a curve over an interval and I've arrived at
$$\int$$ (y⁴ +2y² +1)^1/2 dy
and now I'm pretty sure i should use a u substitution in order to integrate.
I tried using u=y² so du=2y dy so dy=du/2y
Then you have $$\int$$ (u²+2u+1)^1/2 and eventually it boils down to $$\int$$ u+1 du which gives you u²/2 +u

But I think I forgot to incorporate the du/2y and I don't know if I can just change the answer to y²/2 + y.

Any thoughts?

 

[Dick]

You don't have to 'u sub' anything yet. First try and simplify (y^4+2*y^2+1)^(1/2). Isn't y^4+2*y^2+1=(y^2+1)^2? What's the (1/2) power of that?