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I want to find the volume of the region $R$ that lies between

$z= x^2 + y^2, \quad z= 4(x^2 + y^2), \quad z = 1, \quad z = 4$

Using the transformation \begin{align} x &= \frac{r}{t}\cos(\theta)\\ y &= \frac{r}{t}\sin(\theta)\\ z &= r^2 \end{align}

Now, I understand how to do this problem(finding the jacobian, plugging in the transformation, doing the triple integral), but what I don't understand is how to find the bounds for r,t and theta. Is there a general method on how to do this?

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Your region is as follows:

$r\in[2,4]$, $\theta\in[0..2\pi]$, $z\in[2..4]$

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    @amWhy: Unfortunately or fortunately Yes! Life goes on and it needs more attention. Like a wild function, it rules us. :-)2013-04-02