The Trapezoidal Rule

The trapezoidal rule is a method to approximate the area under a line and in doing so approximate the integral of the function represented by that line. The trapezoidal rule is given by the following:

Given an integral, of interval to , where is the function of the line:

The trapezoidal rule is (note this method is an approximation, not exact):

Where:

- is the length of the subinterval
- so if you have 5 intervals on an integral from 0 to 10 than the would be 2
- is the last value of the interval
- given the conditions in the above example the would be 10

When graphed an application of the trapezoidal rule with only 1 interval would look like the following:

Unequal Spacing

If your data set if not spaced equally you can use the following formula:

Where:

- the upper limit, see Summation Notation for more details
- the index value, see Summation Notation for more details
- the change in x

Citations:

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