Bounded x, y, z region for triple integration

V.A. Krasnovsky shared this question 7 months ago
Answered

Hi,

I would like evaluate a triple integral of f(x,y,z) dxdydz, of the bounded region, as per below attachment.


In case you cannot see it, here are the bounds;


0 ≤ x ≤ 4


0≤y≤sqrt(4-z^(2))

0 ≤ z ≤ 2


And for starters, i would like to graph it in 3D.


What i currently see in 3D calculator, is a flat semicircle in the xy plane.

But understandably, the solid should have a height.


Could you pls suggest an approach?


Specifically, i suspect the surface function might work, but i can't figure out how.

It does not accept my inputs.


So I would like the exact syntax for this example, applicable to x,y,z region,


not polar, not cylindrical, not with vectors,


just the plain old x, y, z definitions, as shown above.


Could that be done?


eg. Wolfram evaluates bounded triple integrals easily, but doesn't graph the region.

So i wondered if geogebra could graph it for me.


(I know what this shape should be, but will use the method for more elaborate cases.)


https://www.geogebra.org/3d...


Thanks in advance,

Val

Comments (6)

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1

for this example you can change the orientation of axes doing

0 ≤ x ≤ 4

0 ≤ y ≤ 2

0≤z≤sqrt(4-y^(2))

or to do dydxdz


https://www.geogebra.org/m/jrmzqk5z

Files: foro.ggb
photo
1

Hi,

Thanks!

From the suggested list, i randomly picked "Volumen 6",


it opened in Geogebra Classic,

I plugged in all 3 of my bounds,


and it displayed the expected region. Excellent!


The foro.ggb did not work out as well.

When opened with 3D calculator, it showed a surface vector expression,


and the graph was the circular arc with respect to z, but no other part of the x,y,z bounded region.


Additionally i would like to ask if anyone knows about Geogebra's capacity to evaluate this triple integral, and if yes, which Geogebra? And what's the example syntax pls?


Thanks much for helping.


Best Regards,

Val

photo
photo
1

see CAS view

I work only with classic ver 5

/es1gBD3KlqyopQOEfvCELAeUjBDFUDJCFEPJCFEMJSNEMZSMEMVQMkIUQ8kIUQwlI0QxlIwQxVAyQhRDyQhRDCUjRDGUjBDFUDJCFEPJCFEMJSNEMZSMEMVQMkIUQ8kIUQwlI0QxlIwQxVAyQhRDyQhRDCUjRDGUjBDFUDJCFEPJCFEMJSNEMZSMEMVQMkIUQ8kIUQwlI0QxlIwQxVAyQhRDyQhRDCUjRDGUjBDFUDJCFEPJCFEMJSNEMZSMEMVQMkIUQ8kIUQwlI0QxlIwQxZQj2f8DQ+W+zmSCrrIAAAAASUVORK5CYII=

photo
1

Oh wow, thanks much!


It does work to graph, and evaluate, in CAS, the online version.

I don't know if it's same as vs.5 or not, but regardless, it's cool!

(attached is the screen shot)


Ok, hopefully last q, re: syntax;


$1 and $2 means what within the Integral brackets?


Best,


v.

photo
1

Thank you very much for every part of this feedback.

It was very useful, and fast too.


Be Well,

Val

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1

$2 is the content of cell number 2 in CAS

if you begin cell2 with i.e. c:=integral( then you can write integral(c,0,4) in cell3

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