Here's my question:

**(a)**
$\displaystyle \int^{2 \pi}_0 \int^1_0 [r^2(cos^2\theta + sin^2\theta)]rdr d\theta$

$\displaystyle \int^{2 \pi}_0 \int^1_0 r^3 dr d \theta$ $\displaystyle = \int^{2 \pi}_0 \frac{r^4}{a} |^1_0 d \theta$

$\displaystyle =\frac{1}{4} \theta |^{2 \pi}_0 = \frac{\pi}{2}$

Is this correct?

**(b) **So, is the Jacobian for this problem given by the following?

$\displaystyle

J(x,y)= \frac{\partial(r,\theta)}{\partial (x,y)}=\begin{bmatrix} {\partial r\over \partial x} & {\partial r\over \partial y} \\ {\partial \theta\over \partial x} & {\partial \theta\over \partial y} \end{bmatrix}

$

If so, how can I obtain the four partials in the matrix?