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標題:

MATHS Simpson's Rule

發問:

我想問Simpson's Rule A=w/3(y2+4y3+y4) w=(b-a)/n 個長度1/3(y2+4y3+y4) 點得出黎? 點解有個4係

最佳解答:

冇架﹐積出來的﹐以下是最簡明的証明 We want to derive Simpson's rule for 圖片參考：http://images.planetmath.org:8080/cache/objects/6509/l2h/img1.png We will use Newton and Cotes formulas for 圖片參考：http://images.planetmath.org:8080/cache/objects/6509/l2h/img8.png . The corresponding interpolating polynomial is 圖片參考：http://images.planetmath.org:8080/cache/objects/6509/l2h/img9.png and thus 圖片參考：http://images.planetmath.org:8080/cache/objects/6509/l2h/img10.png Since integration is linear, we are concerned only with integrating each term in the sum. Now, taking 圖片參考：http://images.planetmath.org:8080/cache/objects/6509/l2h/img13.png , we can rewrite the quotients on the last integral as 圖片參考：http://images.planetmath.org:8080/cache/objects/6509/l2h/img14.png and if we calculate the integrals on the last expression we get 圖片參考：http://images.planetmath.org:8080/cache/objects/6509/l2h/img15.png which is Simpson's rule: 圖片參考：http://images.planetmath.org:8080/cache/objects/6509/l2h/img16.png

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我都唔係好明唷 難得咁快有人應 可唔可以教下我|||||中間的strip係double count咗的，所以會有個4出咗嚟。