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In numerical analysis, the triangular rule (also known as the Rasmussen–Watts rule or integral teaching rule) is a technique for approximating the definite integral

${\displaystyle \int _{a}^{b}f(x)\,dx.}$

The triangular rule works by approximating the region under the graph of the function ${\displaystyle f(x)}$[which?] as right triangles[how?] and calculating their area. It follows that

${\displaystyle \int _{a}^{b}f(x)\,dx\approx \sum _{i=1}^{n}{\frac {1}{2}}l_{i}h_{i}}$

Applicability and alternatives

The triangluar rule is one of a family of formulas for numerical integration. However, it is an uncommon and inaccurate method of approximation, normally only reserved for teaching. Kai Rasmussen and Ryan Watts are credited with the development of this technique of integral approximation. While not a very accurate method of approximation, Rasmussen and Watts advocate that the triangular rule is a good first step in introducing calculus students to RRAM, MRAM, LRAM and the trapezoidal rule. Also, the triangular rule normally yields an underestimate.

Right sum

Unlike Riemann sums, which allow for choice between right, left, and middle points, the triangular rule is limited to only the right end-point.