1# Antidifferentiation23If $F'(x)=f(x)$, then $\int f(x) \cdot dx = F(x) + c$45$$\int x^n \cdot dx = {x^{n+1} \over {n+1}} + c, \quad n \in \mathbb{N} \cup \{0\}$$67Rules:89$\int [f(x) \pm g(x)] \cdot dx = \int f(x) \cdot dx \pm \int g(x) \cdot dx$10$\int kf(x) \cdot dx = k \int f(x) \cdot dx$, where $k \in \mathbb{R}$1112## Applications of differentiation to kinematics1314Kinematics - straight line motion of a particle1516Instantaneous velocity - dx/dt