# Solución

El Jacobiano es

$$\begin{aligned} J(r,\theta) &= \frac{\partial(x,y)}{\partial(r,\theta)} = \begin{vmatrix} \frac{\partial x}{\partial r} & \frac{\partial x}{\partial \theta}\\ \\ \frac{\partial y}{\partial r} & \frac{\partial y}{\partial \theta} \end{vmatrix} = \begin{vmatrix} cos \theta & -sen \theta\\ sen \theta & rcos \theta \end{vmatrix}\\ &= r cos^2\theta + r sen^2\theta = r\big(cos^2\theta + sen^2\theta = r \end{aligned}$$