Mathematica Stack Exchange is a question and answer site for users of Mathematica. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

From the iterated integrals $\int_{0}^{1}\int_{\sqrt{y}}^{1}\int_{x^{3}}^{1}f(x,y),$ we have the region $$\Omega=\{0\le y\le1,\sqrt{y}\le x \le 1,x^{3}\le z \le 1\}.$$

How can I use Mathematica to plot $\Omega$?

The following is what I tried.

RegionPlot3D[
  x^3 <= z <= 1 && 0 <= y <= 1 && Sqrt[y] <= x <= 1, 
  {x, 0, 1}, {y, 0, 1}, {z, 0, 1}, 
  PlotStyle -> Directive[Yellow, Opacity[0.5]], 
  Mesh -> None]

But the edge is bad.

share|improve this question
3  
Have you tried RegionPlot3D[]? – J. M. Feb 19 at 13:21
reg = ImplicitRegion[
   0 <= y <= 1 && Sqrt[y] <= x <= 1 && x^3 <= z <= 1, {x, y, z}];
RegionPlot3D[reg, PlotPoints -> 100]

enter image description here

Don't forget the PlotPoints!

share|improve this answer

RegionPlot3D will work fine, you just need to give it the proper region and specify the number of PlotPoints

RegionPlot3D[
 ImplicitRegion[
  x^3 <= z <= 1 && 0 <= y <= 1 && Sqrt[y] <= x <= 1, {x, y, z}], 
 PlotPoints -> 100, Axes -> True]

enter image description here

You can also use DiscretizeRegion

DiscretizeRegion[
 ImplicitRegion[
  x^3 <= z <= 1 && 0 <= y <= 1 && Sqrt[y] <= x <= 1, {x, y, z}]]

enter image description here

Edit ImplicitRegion is also very useful for integration.

Integrate[
 Log[ x y], {x, y, z} ∈ 
  ImplicitRegion[
   x^3 <= z <= 1 && 0 <= y <= 1 && Sqrt[y] <= x <= 1, {x, y, z}]]
(* -(5/12) *)
share|improve this answer
    
There is something error.Your picture is not the region $\Omega$. – AK47 Feb 19 at 13:42
    
@AK47 - sorry, I had copied and pasted the region from your original code. – JasonB Feb 19 at 13:46
    
This might be helpful ! – AK47 Feb 19 at 13:50

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.