Trapezoidal rule
![The function f(x) (in blue) is approximated by a linear function (in red).](/Images/godic/202502/17/Trapezoidal_rule_illustration3520.png")
![An animation showing how the trapezoidal rule approximation improves with more strips.](/Images/godic/202502/17/Trapezium3520.gif")
![Illustration of trapezoidal rule used on a sequence of samples (in this case, a non-uniform grid).](/Images/godic/202502/17/Composite_trapezoidal_rule_illustration.svg3520.png")
In mathematics, and more specifically in numerical analysis, the trapezoidal rule (also known as the trapezoid rule or trapezium rule) is a technique for approximating the definite integral
The trapezoidal rule works by approximating the region under the graph of the function
![f(x)](/Images/godic/202502/17/50bbd36e1fd2333108437a2ca378be623520.png")
as a trapezoid and calculating its area. It follows that