polar coordinates

**studentsteve1202** · April 24th 2008, 01:44 AM

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?

**Moo** · April 24th 2008, 01:50 AM

Hello,

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

**Isomorphism** · April 24th 2008, 01:57 AM

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 $x = r \cos \theta$ and $y = r \sin \theta$ , we will get |r| = 2 (just like you obtained). But then the substitution might yield terms containing $\theta$ too. This $\theta$ can vary from 0 to $2\pi$ for the circle. Thus for the complete specification of the integral we will need these limits of $\theta$ too

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