What commands do I use to get the result as the image?

How can I get what comes out in the image, if possible with the limits of integration.

the solids are for example

$\textbf{x^2+y^2+z^2 =8}$ and $\textbf{z=x^2+y^2}$

I need something like the image, if the integration limits come out better

r1 = Cylinder[{{0, 0, 0}, {0, 0, 30}}, 12];
r2 = Cylinder[{{-20, 0, 15}, {0, 0, 15}}, 10];
r3 = Cylinder[{{20, 0, 15}, {0, 0, 15}}, 10];
r = RegionUnion[r1, r2, r3];
Region[r]


rr1 = RegionIntersection[r1, r2];
rr2 = RegionIntersection[r1, r3];
rr = RegionUnion[rr1, rr2];
Region[rr, PlotTheme -> "Scientific"]


You can use the regions r and rr inside the integration routine.

• Hello I use the version of Mayhematica 10.4, I do not have the commands. What version do you have? – juan muñoz May 11 '18 at 3:32
• @juanmuñoz Try using DiscretizeRegion instead of the Region function. That should be available since v. 10. – MarcoB May 11 '18 at 3:52
• @juanmuñoz, I use V11.1. The Region command just draws the regions defined before. – Rom38 May 11 '18 at 6:25
• two things The second command served me, but when I made the second order, the video controller went down RAM? On the other hand as it is done with these example solidsthe solids $\textbf{x^2+y^2+z^2 =8}$ and $\textbf{z=x^2+y^2}$ – juan muñoz May 12 '18 at 0:19
• That's true, the DiscretizeRegion requires a lot of memory. You can try to play with MaxCellMeasure option inside it to decrease the number of polygons in resulting figure. BTW, it is needed only for drawing of figure. You can use the r and rr for calculations – Rom38 May 12 '18 at 9:26