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Multivariable CalculusEasyChange of Variables & the Jacobian

Change of Variables & the Jacobian · Easy problem

The elliptical polar coordinates x=2rcos⁡θx = 2r\cos\theta, y=3rsin⁡θy = 3r\sin\theta are used to integrate over an ellipse. Find the Jacobian determinant ∂(x,y)∂(r,θ)\dfrac{\partial(x,y)}{\partial(r,\theta)} at r=12r = \dfrac{1}{2}.