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How would you find the arc length of $r(t) = \langle\sqrt{t}, t,t^2\rangle$ for $1\le t\le 4$? This isn't a homework question, I'm just trying to understand how to properly solve a question such as this. I'm working off the textbook Multivariable Calculus by Stewart, and the solutions manual isn't quite explicit on how to do the hardest bits.

I can solve up to the point where: $r'(t) = \sqrt{(1/4t) + 1 + 4t^2}$ but I'm stuck on how to proceed from this point onwards.

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    It doesn't change the difficulty of the problem, but it would be better to have the upper limit something besides $t$ and the derivative of arc length is $s'$, not $r'$ as $r$ has already been used.2012-09-25
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    There's a nice example of how to do this at http://tutorial.math.lamar.edu/Classes/CalcIII/VectorArcLength.aspx2012-09-25

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