# Area and Volume integral using polar coordinates

1. Apr 30, 2012

### izzy93

Hi

I'm working on area and volume integrals. I was wondering, when you convert to do the integral in polar, cylindrical or spherical co-ordinates, is there a standard set of limits for the theta variable in each case?

for example from 0 -pi for polar, 0-2pi for cylindrical?

If not how do you set the limits?

Thankyou

2. Apr 30, 2012

### DonAntonio

It all depends, of course, on the area to be integrated over. If, for example, you want to calculate the area of the

upper semicircle $x^2+y^2=R^2\,,\,\,y\geq 0$ , then upon passing to polar co. you'll have $0\leq \theta\leq \pi$ .

Over other areas you might have have different ranges.

DonAntonio

3. Apr 30, 2012

### izzy93

I see, Thankyou!