# Definite Integrals

The Fundamental Theorem of Calculus For a continuous function $f(x)$ with antiderivative $F(x)$, $$\displaystyle \int_{a}^{b}{f(x)}dx = F(b) – F(a)$$ Properties of Definite Integrals The following properties of definite integrals can all be deductefd from the fundamental theorem of calculus: $\displaystyle \int_{a}^{a}{f(x)}dx = 0$ $\displaystyle \int_{b}^{a}{f(x)}dx = -\int_{a}^{b}{f(x)}dx$ $\displaystyle \int_{b}^{a}{f(x)}dx + \int_{c}^{b}{f(x)}dx = \int_{c}^{a}{f(x)}dx$ \$\displaystyle \int_{b}^{a}{\big[f(x) […]