# Limits of integration on Polar curves

General question, how do you determine the limits of integration of a polar curve? Always found this somewhat confusing and can't seem to find a decent explanation on the internet.

BvU
Homework Helper
What's a polar curve ? A circle on the South pole ? A trajectory described in polar coordinates ?

Oh sorry, any closed curve defined in Polar coordinates. Cardiods, limacons, circles, the works.

BvU
Homework Helper
I should have asked straight away too: What is it you want to integrate ? some function over the surface, over the boundary ? A vector function ? Just the circumference or the area ?

The area enclosed by the Polar curve using Int(1/2 r^2) d theta. I find the determination of the limits of integration slightly ambiguous when I watch any tutorials or read up on Polar coordinates. I normally just use graph trace but I'd like to get an intuitive understanding

BvU
Homework Helper
Browsing some of the links at the lower left might be instructive.
We did a cardioid here not so long ago (no full solution, just hints).
Point is: with a concrete example we can see where things go wrong for you.
normally just use graph trace
and from that, with experience, grows intuition. The latter two aren't sold by weight (in contrast with what some managers seem to think).

I don't think I can provide much guidance based on e.g.
I find the determination of the limits of integration slightly ambiguous
All I can say is usually ##\theta## runs from 0 to ##2\pi## or from ##-\pi## to ##+\pi##. But I doubt if that is helpful for you.

CrazyNeutrino