∫ a b f ( x ) d x = lim n → ∞ ∑ k = 1 n f ( a + b − a n k ) ⋅ b − a n {\displaystyle \int _{a}^{b}f(x)dx=\lim _{n\to \infty }\sum _{k=1}^{n}f(a+{\frac {b-a}{n}}k)\cdot {\frac {b-a}{n}}} = lim n → ∞ ∑ k = 1 n f ( x k ) ⋅ Δ x {\displaystyle =\lim _{n\to \infty }\sum _{k=1}^{n}f(x_{k})\cdot \Delta x} ( Δ x = b − a n , x k = a + k ⋅ Δ x ) {\displaystyle (\Delta x={\frac {b-a}{n}},\;x_{k}=a+k\cdot \Delta x)}