The ApproximateInt(f(x), x = a..b, method = trapezoid) command approximates the integral of f(x) from a to b by using the trapezoidal Rule. The first two arguments (function expression and range) can be replaced by a definite integral.

If the independent variable can be uniquely determined from the expression, the parameter x need not be included in the calling sequence.

Given a partition  of the interval , the trapezoidal rule approximates the integral on each subinterval  by integrating the linear function that interpolates the endpoints  and .  This value is

In the case that the widths of the subintervals are equal, the approximation can be written as

By default, the interval is divided into  equal-sized subintervals.

For the options opts, see the ApproximateInt help page.

This rule can be applied interactively, through the ApproximateInt Tutor.