I need help with determining the limits using cylindrical coordinates
the volume is contained between the surface of a paraboloid z=4-x^2-y^2 and the plane z=0
can anyone help me please??
In converting from rectangular to polar,
$\displaystyle (x-1)^2+y^2<1\implies 0<r<2\cos\vartheta$ and $\displaystyle 0<\vartheta<\pi$
Thus, the double integral in polar coordinates will be $\displaystyle \int_0^{\pi}\int_0^{2\cos\vartheta}\vartheta r\,dr\,d\vartheta$, since $\displaystyle \tan^{-1}\left(\frac{y}{x}\right)=\tan^{-1}\left(\frac{r\sin\vartheta}{r\cos\vartheta}\righ t)=\tan^{-1}\left(\frac{\sin\vartheta}{\cos\vartheta}\right) =\tan^{-1}\left(\tan\vartheta\right)=\vartheta$
--Chris
p.s. From now on, ask new questions in a new thread