+---
+geometry: margin=2cm
+<!-- columns: 2 -->
+graphics: yes
+tables: yes
+author: Andrew Lorimer
+---
+
+# Antidifferentiation
+
+If $F'(x)=f(x)$, then $\int f(x) \cdot dx = F(x) + c$
+
+$$\int x^n \cdot dx = {x^{n+1} \over {n+1}} + c, \quad n \in \mathbb{N} \cup \{0\}$$
+
+Rules:
+
+$\int [f(x) \pm g(x)] \cdot dx = \int f(x) \cdot dx \pm \int g(x) \cdot dx$
+$\int kf(x) \cdot dx = k \int f(x) \cdot dx$, where $k \in \mathbb{R}$
+
+## Applications of differentiation to kinematics
+
+Kinematics - straight line motion of a particle
+
+Instantaneous velocity - dx/dt
+
+## Newton's method
+
+$$x_{n+1}=x_n - {f(x_n) \over f^\prime(x_n)}$$
+
+or
+
+$$x_1=x_0 - {f(x_0) \over f^\prime(x_0)}$$
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