# Dictionary:Trapezoidal rule

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(trap’ ∂ zoid, ∂l) The integral of f between x1 and x2 is approximately equal to the average value times the width:

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

The extended trapezoidal rule applies the rule to subintervals.