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Multivariable CalculusHardChange of Variables & the Jacobian

Change of Variables & the Jacobian · Hard problem

The polar map x=rcos⁡θx = r\cos\theta, y=rsin⁡θy = r\sin\theta has Jacobian determinant ∂(x,y)∂(r,θ)=r\dfrac{\partial(x,y)}{\partial(r,\theta)} = r. Evaluate it at r=3r = 3.