Qurak

N integrate introduction strategies rules and preprocessors

Opplæring 4 steg, kjørt i rekkefølge i én økt. Hvert steg ble kjørt mot motoren, og utdataene nedenfor er det de ga.

Steg 1
NIntegrate[(1/Sqrt[x])Log[(1/x)], {x, 0, 1}, Method -> {"GlobalAdaptive", Method -> "ClenshawCurtisRule"}]
Utdata
4.
Steg 2
NIntegrate[Log[1 + x ^ 2 + y], {x, 0, 10}, {y, 0, 10}, Method -> {"CartesianRule", Method -> {"GaussKronrodRule", "ClenshawCurtisRule"}}]
Utdata
NIntegrate[Log[1 + x^2 + y], {x, 0, 10}, {y, 0, 10}, Method -> {CartesianRule, Method -> {GaussKronrodRule, ClenshawCurtisRule}}]
Steg 3
NIntegrate[Boole[x^2 + y^2 < 1] * (1 - Sqrt[x^2 + y^2]), {x, -1, 1}, {y, -1, 1}, Method -> {"EvenOddSubdivision", Method -> "LocalAdaptive"}]
Utdata
NIntegrate[Boole[x^2 + y^2 < 1]*(1 - Sqrt[x^2 + y^2]), {x, -1, 1}, {y, -1, 1}, Method -> {EvenOddSubdivision, Method -> LocalAdaptive}]
Steg 4
Graphics[{PointSize[0.005], Point[Reap[NIntegrate[Boole[x^2 + y^2 < 1] * (1 - Sqrt[x^2 + y^2]), {x, -1, 1}, {y, -1, 1}, Method -> {"EvenOddSubdivision", Method -> "LocalAdaptive"}, EvaluationMonitor :> Sow[{x, y}]]][[2, 1]]]}, Axes -> True, PlotRange -> {{-1, 1}, {-1, 1}}]
Utdata
-Graphics-

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