更新1:
Using the left end-point no right end-point
integration
2011-02-20 4:47 pm
Using the left end-point as xi* of each subinterval [xi-1, xi] of x, evaluate the definite integral ∫(x+3) dx upper limit is 3 lower limit is 0
回答 (1)
2011-02-20 7:58 pm
✔ 最佳答案
∫(x+3) (from 0 to 3)= lim(n->∞) Σ [xi -1 + 3] [xi - xi-1] ( i from 1 to n where xi = ih and h = 3/n )
= lim(n->∞) Σ [3(i - 1) /n + 3] (3/n)
= lim(n->∞) Σ [9(i - 1) /n^2 + 9/n]
= lim(n->∞) (9/n^2) Σ (i - 1) + 9
= lim(n->∞) (9/n^2)[n(n - 1)/2] + 9
= lim(n->∞) (9/2)(n - 1)/n + 9
= 9/2 + 9
= 27/2
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https://hk.answers.yahoo.com/question/index?qid=20110220000051KK00298