Dictionary:Trapezoidal rule

{{#category_index:T|trapezoidal rule}} (trap’ ∂ zoid, ∂l) The integral of f between x₁ and x₂ is approximately equal to the average value times the width:

$\int _{x_{1}}^{x_{2}}f(x)dx={\frac {1}{2}}(x_{2}-x_{1})\left[f(x_{1})-f(x_{2})\right]$.

The extended trapezoidal rule applies the rule to subintervals.