## 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

1. anonymous

2. anonymous

I need to prove that arc length is represented by that expression, attached as gif file.

3. anonymous

Any ideas are appreciated.

4. 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

5. 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.

6. 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.

7. anonymous

Thanks so much.