Verifying Arc Length of Vector: <2e^t, e^-t, 2t>

[Giuseppe]

Hello, I was wondering if someone could check and see that i did this problem right. You need to find the arc length of the vector from t=0 to 1:

r= <2e^t,e^-t,2t>

So first i took the derivative and got velocity.

v=<2e^t,-e^-t,2>

Next i used the formula for arc length.

arc length = Integral from 0 to 1 of the norm of velocity.

The answer i got was 2e+e^(-1)-3

I am not sure if I am doing my integral right. I'd appreciate to see if someone gets the same answer that I do or tells me if i made a mistake somewhere.
Thanks!

 

[CarlB]

I got a different answer. If I'm right and you're wrong, it's because \int e^{-t} = -e^{-t}, not \int e^{-t} = +e^{-t}. But it's also quite possible that I didn't get the right answer for some other reason.

Anyway, check your work and look for a sign error associated with an integral of e^{-x}. And good luck.

Carl