The composite trapezoidal rule approximates a definite integral by applying the trapezoidal rule
on each of 
equal subintervals. For 
and 
, it is
![int_a^bf(x)dx approx h[(f(x_0)+f(x_n))/2+sum_(j=1)^(n-1)f(x_j)].](/images/equations/CompositeTrapezoidalRule/NumberedEquation1.svg) |
If 
has a continuous second derivative, then for some
the error is
 |
where the error means the exact integral minus its approximation. Thus the method has error 
as 
. In big-O notation,
this means that the error magnitude is bounded by a constant multiple of 
for all sufficiently small positive 
.
