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education/math/MATH1210 (calc 1)/Integrals.md
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@ -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. $= \lim_{n \to \infty} \dfrac{5}{n^2} \sum_{i = 1}^n i$