## The Composite Trapezium Rule

The approximationsand are not very accurate on large intervals (error varying asandrespectively but more accurate approximations can be obtained by breaking the intervalintosubintervals of equal width

Composite Trapezium Rule

Split the intervalintointervals of widthi.e. considerequispaced

pointsThe subintervalis

But sinceand f'' is continuous, there existswithso the error is of the formsince

We can write the composite trapezium rule as

The error is of ordercompared tofor each subinterval.