The discussion revolves around finding the exact length of the polar curve defined by the equation r=2(1+cosθ). Participants note the absence of limits of integration and explore the implications of this in the context of the problem.
Some participants have provided guidance on determining the limits of integration by evaluating the polar curve at specific angles. Others have suggested methods for integrating the resulting expression, including substitution techniques. There is ongoing exploration of the implications of the integral's evaluation over the specified range.
Participants note the lack of explicit limits of integration and question whether the integral setup is correct. The discussion includes references to the shape of the curve and its periodic nature, which may influence the limits chosen for integration.
It's not a good idea to put the statement of the problem only in the title! I started to say "no that is not a problem statement" until I looked up at your title!CitizenInsane said:
Perhaps they expect you to be able to get that yourself. When \theta= 0, cos(\theta)= 1 so r= 4; when \theta= \pi/2, cos(\theta)= 0 so r= 2; when \theta= pi, cos(\theta)= -1 so r= 0; when \theta= 3\pi/2, cos(\theta)= 0 so r= 2 and when \theta= 2\pi, cos(\theta)= 1 so r= 4 again. We make one complete loop around the figure (a "cardiod" since it looks roughly like the "valentine" heart) as \theta goes from 0 to 2\pi. That shouldn't be too surprizing since cosine has period 2\pi.
No, that's correct. Now integrate from 0 to 2\pi.
CitizenInsane said:
