definite integral

The signed area between a curve and the $x$ -axis over an interval, written $\int_a^b f(x)\,dx$ .

The definite integral $\int_a^b f(x)\,dx$ is defined as the limit of Riemann sums as the number of rectangles grows without bound, giving the net signed area between $y=f(x)$ and the $x$ -axis on $[a,b]$ — area above the axis counts positive, below counts negative.

Examples

$\displaystyle\int_0^2 x\,dx = 2$ , the area of the triangle bounded by $y=x$ , the $x$ -axis, and $x=2$ .