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Given a solid described by $S = \{(x,y,z)|0\le x\le4-y^2, -2\le y\le2, 0\le z\le y+2\}$, how do I graph the solid? I have already tried a RegionPlot3D but I might have entered it incorrectly. Any help is appreciated.

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Define the region

R = ImplicitRegion [0 <= x <= 4 - y^2 && -2 <= y <= 2 && 0 <= z <= y + 2, {x, y, z}]

and plot it

RegionPlot3D[R]

enter image description here

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  • $\begingroup$ Just for completeness, a direct RegionPlot3D[0 <= x <= 4 - y^2 && -2 <= y <= 2 && 0 <= z <= y + 2, {x, 0, 4}, {y, -2, 2}, {z, 0, 4}] does the same thing. $\endgroup$ – Roman Jul 16 at 14:54
  • $\begingroup$ Not completely the same, because you have to provide the axes ranges ! $\endgroup$ – Ulrich Neumann Jul 16 at 15:08
  • $\begingroup$ Yes, of course. Your method is easier in that respect. $\endgroup$ – Roman Jul 16 at 15:24

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