- #1
roam
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Homework Statement
Here's my question:
[PLAIN]http://img140.imageshack.us/img140/1500/89319562.gif
The Attempt at a Solution
(a)
[tex]\int^{2 \pi}_0 \int^1_0 [r^2(cos^2\theta + sin^2\theta)]rdr d\theta[/tex]
[tex]\int^{2 \pi}_0 \int^1_0 r^3 dr d \theta[/tex] [tex]= \int^{2 \pi}_0 \frac{r^4}{a} |^1_0 d \theta[/tex]
[tex]=\frac{1}{4} \theta |^{2 \pi}_0 = \frac{\pi}{2}[/tex]
Is this correct?
(b) So, is the Jacobian for this problem given by the following?
[tex]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}[/tex]
If so, how can I obtain the four entries in that matrix?
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