# Bounded x, y, z region for triple integration

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

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

see CAS view

I work only with classic ver 5

$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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