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Math Help - polar coordinates

  1. #1
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    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?
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    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 x+y=4, r is between 0 and 2.
    And an angle has values between 0 and 2 \pi if not, values will be redundant.
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    Quote Originally Posted by studentsteve1202 View Post
    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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