Differential Equations diameter of a spiral

[Goo_Gal1]

how can I calculate the "diameter" of a spiral ? someone told me i need to use Differential or Integral Equations to solve this, but I'm not sure how.

If there is a spiral that it's radius increases by 1 cm for every radian until the radius reaches the size R . how can I calculate the length of the line that the spiral consists of?

 

[mathwonk]

try parametrizing it by angle.

 

[dextercioby]

how can I calculate the "diameter" of a spiral ? someone told me i need to use Differential or Integral Equations to solve this, but I'm not sure how.

If there is a spiral that it's radius increases by 1 cm for every radian until the radius reaches the size R . how can I calculate the length of the line that the spiral consists of?

That's the Spiral of Archimedes.For details check this wonderful site (warning:it's in French):
spiral of Archimedes

Daniel.