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education/math/MATH1210 (calc 1)/Integrals.md

@@ -37,6 +37,11 @@ $$ \int f(x) dx $$
 | $\dfrac{d}{dx} f(x) \pm g(x) = f'(x) \pm g'(x)$       | $\int (f(x) \pm g(x))dx = \int f(x) dx \pm \int g(x) dx$ |
 # Area Under a Curve
 The area under the curve $y = f(x)$ can be approximated by the equation $\sum_{i = 1}^n f(\hat{x_i})\Delta x$ where $\hat{x_i}$ is any point on the interval $[x_{i - 1}, x_i]$, and the curve is divided into $n$ equal parts of width $\Delta x$
+
+Any sum of this form is referred to as a Reimann Sum.
+
+To summarize:
+- The area under a curve is equal to the sum of the area of $n$ rectangular subdivisions where each rectangle has a width of $\Delta x$ and a height of $f(x)$.
 # Definite Integrals
 Let $f$ be a continuous function on the interval $[a, b]$. Divide $[a, b]$ into $n$ equal parts of width $\Delta x = \dfrac{b - a}{n}$ . Let $x_0, x_1, x_2, \cdots, x_3$ be the endpoints of the subdivision.