Find the arc length of the curve?

Question

Find the arc length of the curve defined by r(t)=(t, sqrt(6)/2*t^2, t^3), -1<=t<=1.

r'(t)=<1, sqrt(6)t, 3t^2>

sqrt(1+6t^2+9t^4)

But how do I simplify this?

Answer 1

We can factor 1+6t^2+9t^4 as (1+3t^2)^2

So then we have sqrt [ (1+3t^2)^2) ]

which is just 1+3t^2, which we can now integrate from -1 to 1