The lower sum of a function f relative to a partition P is defined by ｢inf(f(x))ƧP[a,b]｣.ᐥ
┄
U(P) = ｢S⸤i⸥(x⸤i⸥−x⸤i−1⸥) Σi=0,n｣
where S⸤i⸥ = sup{f(x):x⸤i−1⸥≤x≤x⸤i⸥}
L(P) = ｢I⸤i⸥(x⸤i⸥−x⸤i−1⸥) Σi=0,n｣
where I⸤i⸥ = inf{f(x):x⸤i−1⸥≤x≤x⸤i⸥}
┄
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7102 Upper & Lower Sum |
| by EngliSea on 2020-07-16 | |
| ᐥThe upper sum of a function f relative to a partition P is defined by ｢sup(f(x))ƧP[a,b]｣ The lower sum of a function f relative to a partition P is defined by ｢inf(f(x))ƧP[a,b]｣.ᐥ ┄ U(P) = ｢S⸤i⸥(x⸤i⸥−x⸤i−1⸥) Σi=0,n｣ where S⸤i⸥ = sup{f(x):x⸤i−1⸥≤x≤x⸤i⸥} L(P) = ｢I⸤i⸥(x⸤i⸥−x⸤i−1⸥) Σi=0,n｣ where I⸤i⸥ = inf{f(x):x⸤i−1⸥≤x≤x⸤i⸥} ┄ |
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