Qurak

N integrate introduction strategies rules and preprocessors

教學 共 4 個步驟,在同一個工作階段中依序執行。每一步都在引擎上實際執行過,下方的輸出就是它產生的結果。

步驟 1
NIntegrate[(1/Sqrt[x])Log[(1/x)], {x, 0, 1}, Method -> {"GlobalAdaptive", Method -> "ClenshawCurtisRule"}]
輸出
4.
步驟 2
NIntegrate[Log[1 + x ^ 2 + y], {x, 0, 10}, {y, 0, 10}, Method -> {"CartesianRule", Method -> {"GaussKronrodRule", "ClenshawCurtisRule"}}]
輸出
NIntegrate[Log[1 + x^2 + y], {x, 0, 10}, {y, 0, 10}, Method -> {CartesianRule, Method -> {GaussKronrodRule, ClenshawCurtisRule}}]
步驟 3
NIntegrate[Boole[x^2 + y^2 < 1] * (1 - Sqrt[x^2 + y^2]), {x, -1, 1}, {y, -1, 1}, Method -> {"EvenOddSubdivision", Method -> "LocalAdaptive"}]
輸出
NIntegrate[Boole[x^2 + y^2 < 1]*(1 - Sqrt[x^2 + y^2]), {x, -1, 1}, {y, -1, 1}, Method -> {EvenOddSubdivision, Method -> LocalAdaptive}]
步驟 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}}]
輸出
-Graphics-

使用到的函式

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