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How do you set up a double integral for an ellipse in polar coordinates without using Jacobian or Greens Theorem?

I can't seem to figure out what (or if) the limits of r can possible be.

$x = a\cos(t), y = b\cos(t), ( z = 0)$

$x^2/a + y^2/b = 1$

Thank you.

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    The equation of an ellipse in polar coordinates comes out better if you place the pole of the coordinate system at a focus of the ellipse.2012-06-05

2 Answers 2