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Math Help - cartesian to polar integrals

  1. #1
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    cartesian to polar integrals

    can someone help me with this? i don't really understand it. the cartesian double integral is:

    (x^2+y^2)dydx

    and the limits of integration for dy are -sqrt(1-y^2) and sqrt(1-y^2)
    the limits of integration for dx are -1 and 1

    so i know this graph is an ellipse.. but i don't know how to graph it, seeing that it's not an equation (like x^2+y^2=1). so i can't visualize exactly what it is, so i don't know how to visualize the polar graph. agh i'm completely confused. any hints at how to attack this beast?
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  2. #2
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    Quote Originally Posted by isuckatcalc View Post
    can someone help me with this? i don't really understand it. the cartesian double integral is:

    (x^2+y^2)dydx

    and the limits of integration for dy are -sqrt(1-y^2) and sqrt(1-y^2)
    the limits of integration for dx are -1 and 1

    so i know this graph is an ellipse.. but i don't know how to graph it, seeing that it's not an equation (like x^2+y^2=1). so i can't visualize exactly what it is, so i don't know how to visualize the polar graph. agh i'm completely confused. any hints at how to attack this beast?
    The region of integration is a circle with centre at the origin and radius 1. You ought to be able to express this rgion using polar coordinates.

    And you should know what x^2 + y^2 = in polar coordinates. As well, you should know what dx dy becomes in polar coordinates.

    If you need more help please show yiour work and say where you're still stuck.
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