Changes

==Computation==

==Computation==

[[Image:Arc length.jpg|right|197px|thumb|As the length goes to zero, the Pythagorean theorem provides a more and more precise result for the length element ''dL''.]]

[[Image:Arc length.jpg|right|197px|thumb|As the length goes to zero, the Pythagorean theorem provides a more and more precise result for the length element ''dL''.]]

As before, we're not going to be using the Riemann sum definition to compute line integrals.  Let <math>x=x(t),y=y(t)  </math> be a parametric description of <math>C </math>.  This allows us to compute the length element, ''dL'':

As before, we're not going to be using the Riemann sum definition to compute line integrals.  Let <math>x=x(t),y=y(t)  </math> be a parametric description of <math>C </math>, so that ''C'' starts <math>x(t_0),y(t_0)</math> and ends at <math>x(t_1),y(t_1)</math>.  This allows us to compute the length element, ''dL'':

<math>dL = \sqrt{dx^2+dy^2} </math>

<math>dL = \sqrt{dx^2+dy^2} </math>