第5.1节 定积分的概念及性质.pdfVIP

§5.1 §5.1 5.1.1 f (x) [a, b] [a, b] a x x Lx x Lx b 0 1 i−1 i n [a, b] n [x , x ] [x , x ] [x , x ] 0 1 1 2 n−1 n ∆xi xi −xi−1 (i 1, 2, L, n) λ max{∆x , ∆x , L, ∆x } 1 2 n n n ξ ∈[x , x ] (i 1, 2, L, n) ∑f (ξ )∆x lim ∑f (ξ )∆x i i−1 i i i i i λ→0 i 1 i 1 b f (x) [a, b] f (x) [a, b] f (x)dx ∫ a b n f (x)dx lim ∑f (ξ )∆x ∫a λ→0 i i i 1 f (x) x a b [a, b] b 1 ∫a f (x)dx f (x) [a, b] 2 ξ i 5.1.2 1f (x) [a, b] f (x) [a, b] 2f (x) [a, b] f (x) [a, b] 3f (x) [a, b] f (x) [a, b] 4 b 5.1.3 ∫a f (x)dx y f (x) x a, x b x