# [✓] Calculate the volume of an exponentially distorted ellipsoid?

Posted 6 months ago
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 Consider the following code: a = 2; b = 1.5; c = 1; tx = 0.175; ty = 0.2; tz = 0.25; AbsoluteTiming[ Volume[ImplicitRegion[ Exp[tx*x] (x/a)^2 + Exp[ty*y] (y/b)^2 + Exp[tz*z] (z/c)^2 <= 1, {x, y, z}], Method -> "NIntegrate"]] {39.1684, RegionMeasure[ ImplicitRegion[ 1/4 E^(0.175 x) x^2 + 0.444444 E^(0.2 y) y^2 + E^(0.25 z) z^2 <= 1, {x, y, z}], 3, WorkingPrecision -> MachinePrecision, Method -> "NIntegrate"]} 
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Posted 6 months ago
 Alternative way:  \$Version (* "11.3.0 for Microsoft Windows (64-bit) (March 7, 2018)" *) a = 2; b = 1.5; c = 1; tx = 0.175; ty = 0.2; tz = 0.25; R = ImplicitRegion[Exp[tx*x] (x/a)^2 + Exp[ty*y] (y/b)^2 + Exp[tz*z] (z/c)^2 <= 1, {x,y, z}]; V = DiscretizeRegion[R, Method -> "RegionPlot3D"] // Quiet; Volume[V] (* 6.924361674 *) or: a = 2; b = 1.5; c = 1; tx = 0.175; ty = 0.2; tz = 0.25; AbsoluteTiming[N[Volume[ImplicitRegion[Exp[tx*x]*(x/a)^2 + Exp[ty*y]*(y/b)^2 + Exp[tz*z]*(z/c)^2 <= 1, {x, y, z}]]]] (* {202.8073994, 6.924361674} *)