1. ## polar coordinates

Hey can anybody help with polar coordinates?
when you are doing a double integral and you have x^2+y^2=4. This means that r is equal to 2 so one of the integrals is bounded by the limits 2 and 0. however i am not sure how to find out the other limits to the integral. Apparantly it is 2(pi) (not sure how to get the symbol up!) and 0. but i dont know how to get this. Can anybody help?

2. Hello,

Because when using polar coordinates, you have a function $\displaystyle f(r,\theta)$ where r is the distance between the center and the point and $\displaystyle \theta$ the angle.
Since it's bounded by x²+y²=4, r is between 0 and 2.
And an angle has values between 0 and $\displaystyle 2 \pi$ if not, values will be redundant.

3. Originally Posted by studentsteve1202
Hey can anybody help with polar coordinates?
when you are doing a double integral and you have x^2+y^2=4. This means that r is equal to 2 so one of the integrals is bounded by the limits 2 and 0. however i am not sure how to find out the other limits to the integral. Apparantly it is 2(pi) (not sure how to get the symbol up!) and 0. but i dont know how to get this. Can anybody help?
Remember that there are 2 variables. In one dimension, we used to tell the corresponding section of the line(x-axis) to get a particular area. In two dimension, we have to specify a section of the plane. So in this case its the circle x^2 + y^2 = 4. So if we do the substitution $\displaystyle x = r \cos \theta$ and $\displaystyle y = r \sin \theta$, we will get |r| = 2 (just like you obtained). But then the substitution might yield terms containing $\displaystyle \theta$ too. This $\displaystyle \theta$ can vary from 0 to $\displaystyle 2\pi$ for the circle. Thus for the complete specification of the integral we will need these limits of $\displaystyle \theta$ too