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roadrunner
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Homework Statement
"Reparameterize the curve with respect to the arc length measured from the point where t=0 in the direction of increasing t. r(t)=e^(2t)*cos2t i +2 j + e^(t2)*sin2t k"
Homework Equations
The Attempt at a Solution
the method we were taught is take r'(t) and then find |r'(t)| and then integrate that.
but in every example we were given, the derivative was a real number, not a function (IE: 12, sqrt(23) etc)
i took the derivative and got [-2e^(2t)sin(2t)+2te^(2t)cos(2t)]i +0j + [2e^(2t)cos(2t)+2te^(2t)sin(2t)] k
then |r'(t)|=(after simplifying it i got) =2e^(2t)sqrt(1+t^2) which seems nice and simple now...but how to i integrate that...
the form they used was s=s(t)=integral from 0-t of |r'(u)|du
for every other problem of this nature