# Why function in multivariable integration limits: "not machine-sized #" ?

GROUPS:
 RegionPlot3D[Abs[Sin[z]] r, {r, 0, Sqrt[Cos[2 \[Theta]]]}, {\[Theta], 0, \[Pi]/4}, {z, 0, 2 \[Pi]}, PlotRange -> Automatic] Trying to plot this returns error: ""Limiting value Sqrt[Cos[2\[Theta]]] in {r,0,Sqrt[Cos[2\[Theta]]]} \is not a machine-sized real number""Looking through all the different 3DPlot types...did not find any examples of functions in the limits of multivariable integration...?I'm converting from Maple10, which does not have any problem plotting the above. Mathematica11 will integrate a multivariable with the function in the limits...but no-go on plotting?
 Valeriu Ungureanu 1 Vote In my opinion, there are two errors in your code. First, the interval for $r$ must be written correctly in the form specified by the documentation:In your code $r_{max}$ must be a number, but not a variable expression dependent of $\Theta$ and $z$.Second, the expression for RegionPlot3D[] must be an inequality. So, by providing these two corrections and fixing $r_{max}$ to value $1.2 Sqrt[\pi/4]$, the code RegionPlot3D[ Abs[Sin[z]] <= r, {r, 0, 1.2 Sqrt[\[Pi]/4]}, {\[Theta], 0, \[Pi]/ 4}, {z, 0, 2 \[Pi]}, PlotRange -> Automatic] generates the following graph:Sure, the code becomes more interesting if we use the function Manipulate[]: Manipulate[ RegionPlot3D[ Abs[Sin[z]] <= r, {r, 0, rmax}, {\[Theta], 0, \[Pi]/4}, {z, 0, 2 \[Pi]}, PlotRange -> Automatic], {rmax, 0.1, 3}] 
 Thanks Valeriu, Actually I was able to get the result I was looking for with: RevolutionPlot3D[{(Sqrt[Cos[2*\[Theta]]])*Sin[t], t}, {t, 0, 2 Pi}, {\[Theta], -Pi/4, Pi/4}] `This is the exact same code as Maple10 plot3d cylindrical coordinates, so perhaps RevolutionPlot3D could be called cylindrical coordinates.