This is what it is and how to use the trapezoidal rule in Excel.

## What Is The Trapezoidal Rule?

The trapezoidal rule is a numerical method for approximating the definite integral of a function. We use the trapezoidal rule to estimate the integral of a function; that is to estimate the value of intervals of one or more variables.

The rule works by evaluating the area under a curve after first dividing the total area into smaller trapezoids. From there, we can calculate the area.

## How to calculate the Trapezoidal Rule?

The steps below will take you through the process to create a table to chart a curve. A quick reference guide is available at the end of this document.

Open the spreadsheet **How To Use The Trapezoidal Rule In Excel - Sample Data, go **to **Sheet 1**.

Create a table containing the variables and their range. We will use the values 0 – 6 as our limits of integration.

Determine for each interval how many subintervals you want. We will use 2 subintervals per interval or 1/2 =.5. The more slices used increases the accuracy of the result.

Using the subintervals identified enter the range of values in the column with the heading '**x**'. Example list the values 1 through x, x being the upper value of the range you want to analyze.

Make the following entries:

**B2**-**x**, this is the column heading**B3**–**1****B4**-**5**

Select both **B3** and **B4**, left click the fill handle then drag the handle down to **B13**. This covers the range we identified.

Label the next column. In **C2**, type the column heading **f(x)=1/x**; the formula for this column.

Divide 1 by each of the intervals. In **C3** type **=1/B3,** press enter.

Use the fill handle to copy this formula to the cells of this column.

Label the next column. In **D2** type the heading** Area for each interval.**

Under the heading skip the first cell, in the next cell (**D4**).

Type this formula **=(0.5)*(C3+C4)*0.5.**

Use the fill handle to copy to the rest of this column.

Total the values in the **Area for each interval**.

In cell **D14 **type **=SUM(D3:D13), **press** enter**.

## Quick reference guide

- We will use specific cell addresses in this guide to make the steps easier to follow.
- Open a new spreadsheet, add the following column headings: -
**B3 - x****C3 - f(x)=1/x****D3 - Area for each interval.**- Determine the limits of integration, for example, 1 - 6
- Determine for each interval how many subintervals you want. For example, if you want 2 subintervals, Divide 1 by 2 =.5.
- Under column
**‘x’**, List the integration range in the increments you decided. In this example 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6. - Divide 1 by each of the intervals. In
**C4**type**=1/B3,**press enter. Use the fill handle to copy this formula to the cells of this column. **Area for each interval**- skip the first cell in this column, in the next cell (**D5**), type this formula**=(0.5)*(C4+C5)*0.5.**Copy the formula to the remaining cells in this column.- Total the values in the
**Area for each interval**In cell**D15**type**=SUM(D4:D14),**press**enter**.