Area and Volume integral using polar coordinates

[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

 

[DonAntonio]

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

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

 

[izzy93]

I see, Thankyou!