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displacement is vector formed be integrating the i, j, and k components separately and the distance traveled is the integral of the magnitude.
so displacement s should =
or would you just evaluate r from 0 to ln3 for displacement then the integral of the v would be distance
o wait sorry i thought r was velocity for a second r itself is displacement and the ittegral of the magnitude of v is distance traveled
where v =(dr1/dt, dr2/dt, dr3/dt)
yeah thats what I was thinking so it just needs to be evaluated. and take the derivitive of r to get v and take the magnitude of that for the distance correct
but you have to find the integral of the magnitude of v not just the magnitude itself
and i assume you know this but jsut in case magnitude is the positive square root of the sum of each component squared
ok so i took the sqrt of each component squared after taking dy/dx of r. I then end up with sqrt((e^t)^2+(-e^(-t))^2+sqrt(2)^2) as the magnitude. So from there I must take the integral of this. It seems like the magnitude must not be correct because its a difficult integration
you might be required to use numerical integration