Category: Classwork

Definition: The Definite Integral.

If $f(x)$ is a function defined on an interval $[a,b]$, the definite integral of $f$ from $a$ to $b$ is given by

$${\int }_a^{b}f(x)dx=limn\to \mathrm{\infty }\sum _{i=1}^{n}f\left(x_i^{\ast }\right)\mathrm{\Delta }x$$

provided the limit exists. If this limit exists, the function $f(x)$ is said to be integrable on $[a,b]$, or is an integrable function.