Find the Arc Length of a Curved Line

[zacman2400]

Homework Statement

find the arc length
x=2e^t, y=e^-t, z=2t

Homework Equations

The Attempt at a Solution

dr/dt=2e^ti-e^-tj+2
ds/dt=sqrt((4e^2t)+(e^-2t)+4)) dt
=integral from 0 to 1 sqrt(4e^4t+4e^2t+1)/e^t
sorry about the lack of latex, I have no idea how to integrate this function

 

[NJunJie]

you have got it right.
why not try splitting them out. Take out the power and apply linearity rule to each integrand?

 

[Mark44]

Homework Statement

find the arc length
x=2e^t, y=e^-t, z=2t

Homework Equations

The Attempt at a Solution

If you don't know LaTeX, at least use some spaces to make what you have written more readable.

dr/dt=2e^ti-e^-tj+2

Don't you mean
dr/dt = 2e^t i - e^(-t) j + 2k?

ds/dt=sqrt((4e^2t)+(e^-2t)+4)) dt

Are you sure about the middle term in the radical above?

=integral from 0 to 1 sqrt(4e^4t+4e^2t+1)/e^t

Shouldn't your integrand be ds/dt * dt?

sorry about the lack of latex, I have no idea how to integrate this function