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3

Here is a way to do what you want using DiscretizeGraphics as suggested by @user21. No need to call NDSolveFEM` r = RegionDifference[Ball[{0, 0, 0}], Ball[{0, 0, 1}]] rp = RegionPlot3D[r, PlotPoints -> 50] Now we discretize the Graphics object with the following clever replacements that somehow works: DiscretizeGraphics[Normal[rp /. {(PlotRange ...


4

Here is a workaround: r1 = RegionDifference[Rectangle[{0, 0}, {10, 10}], Rectangle[{4, 4}, {8, 8}]]; r2 = TransformedRegion[r1, RotationTransform[45 \[Degree], {5, 5}]]; mr = DiscretizeRegion[r2] And then: RegionPlot[mr]


12

In principal you should be able to do r = RegionDifference[Ball[{0, 0, 0}], Ball[{0, 0, 1}]]; rp = RegionPlot3D[r, PlotPoints -> 50]; DiscretizeGraphics[rp] Unfortunately, this does not work and is hopefully improved in a future version. One thing you can do, however, is use the finite element mesh generator for this: Needs["NDSolve`FEM`"] m = ...


0

The way you wrote it it obviously vanishes, since all the conditions are on $y^2$ while the integrand is $y$ (so whatever the $y>0$ bit contributes is cancelled by the $y<0$ bit). If you meant for $y>0$ to be true, then eg Integrate[y*Boole[z^2 + 6 < y^2] Boole[y^2 < 5 z] Boole[0 < y], {y, -\[Infinity], \[Infinity]}, {z, ...


3

If I understand your question correctly - as judged from the text typed - the answer should read (writing - 6x instaed of just - 6 as some others have done, put the function in brackets before multiplying with Boole, also use +- Infinity which is better than some arbitrary (?) finite value like +-2) Integrate[(y^2 - 2*x^2*y + 6*x^3 - 3*x*y + 2*y - 6*x)* ...


3

Amplifying on the answer by Chenmingi: Boole will automatically restrict the integral to the appropriate region so you can integrate from -Infinity to Infinity for each of the variables. int1 = Integrate[ (y^2 - 2 x^2 y + 6 x^3 - 3*x*y + 2 y - 6) * Boole[y >= 2*x^2 - 2 && y <= 3*x], {x, -Infinity, Infinity}, {y, -Infinity, Infinity}] ...


5

Clear["Global`*"] expr = y^2 - 2 x^2 y + 6 x^3 - 3*x*y + 2 y - 6; Integrate[ expr Boole[y >= 2*x^2 - 2 && y <= 3*x], {x, -Infinity, Infinity}, {y, -Infinity, Infinity}] -(36625/2688) Reduce[y >= 2*x^2 - 2 && y <= 3*x, y] (x == -(1/2) && y == -(3/2)) || (-(1/2) < x < 2 && -2 + 2 x^2 ...



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