- #1
irycio
- 97
- 1
Homework Statement
Calcualte the value of [tex]\int\limits_L \sqrt{x^2+y^2}dl[/tex], where L is an arc of a logarithmic spiral [tex]r=ae^{m\phi}[/tex] between points A(0,a) and B([tex]-\infty[/tex],0).
Problem: I can't find a value of [tex]\phi[/tex] where x=[tex]-\infty[/tex] or y=a.
Homework Equations
We parametrise and get:
[tex]x=ae^{m\phi}\cos(\phi)[/tex]
[tex]y=ae^{m\phi}\sin(\phi)[/tex]
The Attempt at a Solution
Well, I guess I can't do much without the boundaries. I typed the equation for y=a into mathematica and got error messages, more or less the same for function Solve and Reduce (that the equation can not be solved using algebraic methods).
Obviously, the equation x=[tex]-\infty[/tex] doesn't give any result either. Help, please!