The Integral

Definition

For a function $f(x)$ which is defined on the interval $[a,b]$, then the integral of that function is

$$li{m}_{n\to \infty }\sum _{i=0}^{\infty }f(x_i)\Delta x={\int }_a^{b}f(x)dx$$

Derivation

The integral originally solved the problem of finding the areas of certain geometric shapes or curves; introductory explanations of the integral still approach by this route.