The definite integral equals the area of the region between the graph of the function and the x-axis over the interval [a,b].
Symbols
P
area
a,b
limits of integration
f(x)
integrand
Where it comes from
The definite integral sums infinitely many thin rectangles under the graph — giving the area between the curve and the x-axis. It is the inverse operation to differentiation.
When to use it
Area under a graph, distance from velocity, work from force.