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
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.