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anonymous
 5 years ago
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
anonymous
 5 years ago
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

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I need to prove that arc length is represented by that expression, attached as gif file.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Any ideas are appreciated.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I'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
 5 years ago
Best ResponseYou've already chosen the best response.0Thanks 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
 5 years ago
Best ResponseYou've already chosen the best response.0we 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.
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