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

 

[quicknote]

Hi there,

I have checked your solution and it looks correct to me. Your use of the derivative to find the velocity and the formula for arc length is correct. I also got the same answer of 2e+e^(-1)-3 when I did the integral. Great job! Keep up the good work in your calculations and problem solving. If you have any further questions or need clarification, please don't hesitate to ask. Keep up the good work!