anonymous
  • anonymous
What is the arc length of function r(t) =
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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experimentX
  • experimentX
arc length from where to where?
anonymous
  • anonymous
This isn't a calc 2 problem
zepdrix
  • zepdrix
The arc length of a vector valued function is defined to be:\[\large L\qquad=\qquad \int\limits |r'(t)|dt\] So we start with, \[\large r(t)\qquad=\qquad \left\]Taking the derivative of the components gives us, \[\large r'(t)\qquad=\qquad \left\] From here we want to find the magnitude of the derivative function, \[\large |r'(t)| \qquad=\qquad \sqrt{\left(e^{t-3}\right)^2+\left(-3t^{-2}\right)^2} \qquad=\qquad \sqrt{e^{2t-6}+9t^{-4}}\] So that's the thing we'd integrate... hmmm.. But as experiment asked, where are we integrating from and to? You said at t=3, but that doesn't make much sense. Did you mean from t=0 to t=3?

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anonymous
  • anonymous
Thanks to both @experimentX and @zepdrix ! I got it :)
experimentX
  • experimentX
you can express it as a function of t ... if it is what you might mean \[ \int_t^3 |r'(t)|dt\]

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