# Thread: can't solve this arc length integral

1. ## can't solve this arc length integral

find the length of the curve of r(t)=<2t, t^2, (t^3)/3>

so i take the derivative of each, and then square them and get

<4, 4t^2, t^4>

and the formula is srqt (4+4t^2+t^4)

and i need to find it from t=1 to t-2.

i just don't know how to solve that integral. it doesn't really seem possible. can anyone help with that? thanks

2. Originally Posted by isuckatcalc
find the length of the curve of r(t)=<2t, t^2, (t^3)/3>

so i take the derivative of each, and then square them and get

<4, 4t^2, t^4>

and the formula is srqt (4+4t^2+t^4)

and i need to find it from t=1 to t-2.

i just don't know how to solve that integral. it doesn't really seem possible. can anyone help with that? thanks
Hint: $t^4+4t^2+4 = (t^2+2)^2$.

Now can you proceed?

3. ah, always a simple solution. thanks for pointing that out!