I computed $s= \int_{-\infty}^t \! |r'(u)| \, \mathrm{d} u$ to be $s=\sqrt{38e^{2t}}$. Solving for t yields $t=\ln\left(\sqrt{\frac{s^2}{38}}\right)$. The online homework system I'm using isn't accepting the answer after substituting this value into the original vector function.
Find the arc length parameterization of $r(t)=\langle e^t\sin t,e^t\cos t,6e^t\rangle$.
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multivariable-calculus
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0Maybe the computer doesn't like $\sqrt{s^2}$ where $s$ will do. Though I would expect it to test correctness by substituting random values. – 2012-10-02
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0I've tried several different forms of the answer, including putting a constant 0.5 outside the logarithm and simplifying $\sqrt{s^2}$ to s. – 2012-10-02