Hi,

I have a triple integral and i would like to plot it in Mathematica to understand the object and the implications of its volume under the curve.

It's easy to integrate and the answer is 57375 / 64.

The triple Integral is as follows:

? ? ? x^3 * y^5 * z dxdydz z = (1,2); y = (z, 4z); and x = (z/y, 2z/y)

I have done the following, most of the syntax i copied from another demonstration but i still think it is not the real shape of the object in question:

r = ImplicitRegion[{z > 0, y > 0, z >= 0}, {x, y, z}];
 i = HoldForm[
    Integrate[x^3*y^5*z, {z, 1, 2}, {y, z, 4*z}, {x, z/y, 2*z/y}]];
 cp = ContourPlot3D[{z, y, z}, {x, 0, 40}, {y, 0, 40}, {z, 0, 40}, 
    Mesh -> None, ContourStyle -> {Red, Green, Blue, Orange}, 
    PlotLegends -> "Expressions"];
 rp = RegionPlot3D[r, PlotPoints -> 100, Background -> Black];
 TraditionalForm[
  Column[{r, Row[{i, "=", ReleaseHold[i]}], 
    Row[{"Volume[r]= ", Volume[r]}], Row[{cp, rp}]}, 
   Alignment -> Center]]

Can someone help me to plot the actual object in 3D?

Thanks