diff --git a/education/math/MATH1210 (calc 1)/Integrals.md b/education/math/MATH1210 (calc 1)/Integrals.md index 016a988..e68ab66 100644 --- a/education/math/MATH1210 (calc 1)/Integrals.md +++ b/education/math/MATH1210 (calc 1)/Integrals.md @@ -58,8 +58,8 @@ $f(x_i)$ is the *height* of each sub-interval, and $\Delta x$ is the change in t Relevant formulas: $$ \sum_{i = 1}^n = \dfrac{(n)(n + 1)}{2} $$ -$ \Delta x = \dfrac{1 - 0$ -1. $\int_0^1 5x \space dx = \lim_{n \to \infty} \sum_{i=1}^n 5(x_i) * \Delta x$ +$$ \Delta x = \dfrac{1 - 0}{n} = \dfrac{1}{n}$$$$ x_i = 0 + \Delta xi + \dfrac{1}{n} \cdot i$$ +1. $\int_0^1 5x \space dx = \lim_{n \to \infty} \sum_{i=1}^n 5(x_i) \cdot \Delta x$ 2. $= \lim_{n \to \infty} \sum_{i=1}^n 5(\frac{1}{n} \cdot i) \cdot \frac{1}{n}$ 3. $= \lim_{n \to \infty} \sum_{i = 1}^n \dfrac{5}{n^2}\cdot i$ 4. $= \lim_{n \to \infty} \dfrac{5}{n^2} \sum_{i = 1}^n i$