# How to draw integral with mathematica

• Mathematica

## Main Question or Discussion Point

Hello,
is there a way to draw the volume of a triple integral????, and in different ways???(rectangular, cylindrical and sphere coordinates)
for example if the integral is

what I want is to draw directly with the above formula

I have been struggling all day with this, because if for example I use something like Plot3D[Integrate[x..... it will first solve the integral, which will become a constant and then draw that constant

Also there must be a way because in the calculus book I'm studying, in many exercises it ask you to draw the volume of the problem with a software tool

Thank you, I really need this

#### Attachments

• 9.5 KB Views: 1,389
• 18.3 KB Views: 1,266

## Answers and Replies

Related MATLAB, Maple, Mathematica, LaTeX News on Phys.org
Dale
Mentor
What you want to plot here is not the integrand nor the integral, what you want to plot is the limits of integration. I would use ParametricPlot3D or RegionPlot3D, but you will have to transform from spherical coordinates to Cartesian coordinates either way.

Thank you DaleSpam, now I can draw integrals in rectangular coordinates, for example, the integral

RegionPlot3D[-2 < x < 2 && -\[Sqrt](4 - x^2) < y < \[Sqrt](4 - x^2) && x^2 + y^2 < z < 4, {x, -2, 2}, {y, -2, 2}, {z, 0, 5}, PlotPoints -> 50, Mesh -> True, AxesLabel -> Automatic]
will draw

but for spherical coordinates, I found the sentence SphericalPlot3D, which for example with
SphericalPlot3D[{1}, {\[Phi], 0, Pi/4}, {\[Theta], 0, 2 Pi}]
will draw

but I doesn't draw the cone underneath the sphere, my question is, is there a way to do that???

I thought something like saying to mathematica "draw me rho from 0 to 1 continuously ", and it would draw

, but the cone being solid

thank you

#### Attachments

• 22.8 KB Views: 1,466
• 20.4 KB Views: 1,063
• 18.3 KB Views: 1,241
• 22.8 KB Views: 401
• 18.3 KB Views: 378
Hepth
Gold Member
I'd use region plot and just use spherical coordinates. Its slower, and requires tweaking due to the angles but :

r = Sqrt[x^2 + y^2 + z^2];
\[Phi] = ArcTan[y/Abs[x]];
\[Theta] = ArcCos[Abs[z]/Sqrt[x^2 + y^2 + z^2]];
RegionPlot3D[
0 < r <= 3 && 0 < Abs[\[Theta]] < \[Pi]/4, {x, -5, 5}, {y, -5,
5}, {z, 0, 5}, PlotPoints -> 60, Mesh -> True,
AxesLabel -> Automatic, PlotRange -> {{-3, 3}, {-3, 3}, {-1, 5}}]

http://en.wikipedia.org/wiki/Spherical_coordinates

Same for cylindrical. You just have to do a coordinate conversion back to cartesian.