# I Limits of integration on Polar curves

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1. Mar 6, 2017

### CrazyNeutrino

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.

2. Mar 6, 2017

### BvU

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

3. Mar 6, 2017

### CrazyNeutrino

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

4. Mar 6, 2017

### BvU

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 ?

5. Mar 7, 2017

### CrazyNeutrino

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

6. Mar 7, 2017

### BvU

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.
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.