New in Wolfram Mathematica 6: New Generation Numerical Integration
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Choose between State-of-the-Art Methods

In addition to its automatic algorithm selection,* Mathematica* 6 provides detailed control over methods used. This shows successive points sampled in four different methods.

In[1]:= | GraphicsGrid[ Partition[ Graphics3D[{Opacity[.5], Line[Block[{t = 0}, Reap[Quiet@ NIntegrate[Sqrt[x] + Sqrt[y], {x, 0, 1}, {y, 0, 1 - x^2}, EvaluationMonitor :> Sow[{x, y, t++}], Method -> #]][[2, 1]]]]}, BoxRatios -> 1] & /@ {Automatic, "LocalAdaptive", "QuasiMonteCarlo", "AdaptiveQuasiMonteCarlo"}, 2]] |

Out[1]= |