The discussion focuses on calculating the arc length of a parametric curve defined by the equations x=2e^t, y=e^-t, and z=2t. The derivative of the position vector dr/dt is correctly identified as 2e^ti - e^-tj + 2k. The expression for ds/dt is derived as sqrt(4e^2t + e^-2t + 4), leading to the integral from 0 to 1 of sqrt(4e^4t + 4e^2t + 1)/e^t dt. Participants emphasize the importance of clarity in mathematical notation and suggest using the linearity rule for integration.
PREREQUISITESStudents in calculus, mathematicians, and anyone involved in physics or engineering who needs to compute arc lengths of curves in three-dimensional space.
If you don't know LaTeX, at least use some spaces to make what you have written more readable.zacman2400 said:Homework Statement
find the arc length
x=2e^t, y=e^-t, z=2t
Homework Equations
The Attempt at a Solution
Don't you meanzacman2400 said:dr/dt=2e^ti-e^-tj+2
Are you sure about the middle term in the radical above?zacman2400 said:ds/dt=sqrt((4e^2t)+(e^-2t)+4)) dt
Shouldn't your integrand be ds/dt * dt?zacman2400 said:=integral from 0 to 1 sqrt(4e^4t+4e^2t+1)/e^t
zacman2400 said:sorry about the lack of latex, I have no idea how to integrate this function