Range of integration polar equations

[burt]

Is the range of a polar equation always from \(0\) to \(2\pi\)? Or is it sometimes less/more than that? Like is the range of integration for a rose curve with an odd n - only until \(\pi\)?

 

[Dr.Peterson]

It depends on the problem. Presumably you are talking about finding area (which is not what "range of an equation" would mean); you need to determine what values of theta it takes to trace out the area you want.

In addition, you have to consider where r is positive or negative -- just as in finding the area between a curve and the x-axis, you would need to consider whether it crosses the axis and integrate each part separately.

 

[burt]

resumably you are talking about finding area

True - I should've used better language - not sure what would be the proper term usage though.