anonymous
  • anonymous
Show that the arc length of a path in polar coordinates (r,θ), where both coordinates depend smoothly on t, is represented by the integral expression
Mathematics
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anonymous
  • anonymous
Show that the arc length of a path in polar coordinates (r,θ), where both coordinates depend smoothly on t, is represented by the integral expression
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
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anonymous
  • anonymous
I need to prove that arc length is represented by that expression, attached as gif file.
anonymous
  • anonymous
Any ideas are appreciated.

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anonymous
  • anonymous
I'm sure this is it? http://tutorial.math.lamar.edu/Classes/CalcII/PolarArcLength.aspx I haven't looked into the derivations.. But it's all there! good luck
anonymous
  • anonymous
Thanks for the link, but it gives me the arc length integral in terms of dθ instead of dt. The integral expression that i need to show is for dt.
anonymous
  • anonymous
we have x= rcos theta , y= r sin theta dx/dt=dr/dt(cos theta) -r sin theta (d theta/dt) dy/dt=dr/dt(sin theta) +r cos theta (d theta/dt) v^2= (dx/dt)^2+(dy/dt)^2 s=int_{t0}^{t1}vdt (dx/dt)^2+(dy/dt)^2=(dr/dt)^2+(r*d theta/dt)^2 hence you get the expression.
anonymous
  • anonymous
Thanks so much.

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