How to Use the Trapezoidal Rule in Microsoft Excel

Learn how to use Excel to approximate the integral of a function.
••• graph image by Roman Sigaev from Fotolia.com

The trapezoidal rule is used to approximate the integral of a function. The rule involves treating the area under a curve as a series of trapezoidal slices. Implementing this rule in Excel requires inputting a curve's independent and dependent values, setting integration limits, setting slice parameters and using a function to determine area.

    Input the curve you wish to analyze in an Excel spreadsheet. Put the independent values (i.e., x values) in the first column. Put the dependent values (i.e., f[x] values) in the second column.

    Determine the desired limits of integration. For example, if you want to find the area under a curve between x = 0 and x = 5, your limits of integration are 0 and 5.

    Delete any values outside the limits of integration in the first two columns of your table.

    Determine the desired number of trapezoidal slices. Divide this value by the range of your integration limits to get slice length. For example, if you want five slices between x = 0 and x = 5, your slice length will be one.

    Delete all independent values that are not either an integration limit or a multiple of the slice length. Delete all corresponding dependent values.

    Create a function in the top box of the third column: one-half the slice length times the sum of f[x] and f[x+1]. If your dependent values start in the first row and second column, type (1/2)(slice length)(B1+B2).

    Drag the bottom right of this function box down until the third column is one value short of the first two columns.

    Sum the values of the third column to get the approximate value of your integral.

    Tips

    • As an example of what you should delete, if you erase x = 2.5, you should also erase the corresponding f[x = 2.5].

      When you delete anything from the first or second columns of your spreadsheet, move the remaining values together so the only value with empty boxes under it is the last one.

      To start creating a function in Excel, click on a box and press the "=" key. Press "Enter" when you're finished typing the function.

      If your dependent values start on a different row or column, use those alpha-numeric parameters for your trapezoidal function. For example, if your values start in the third row and third column, use C3 and C4 for initial parameters.

      When you drag the function box down, the other boxes will fill in automatically. If the other boxes display an error message, you have typed the function incorrectly.

      To sum the third column's values, click on any empty box, type "= SUM(", highlight the third column, type ")" and press "Enter."

Related Articles

How to Write Functions in Math
How to Straighten an Inverse Curve
How to Calculate Riemann Sums
How to Make Excel Calculate the Graph's Slope
How to Calculate Pearson's R (Pearson Correlations)...
How to Find the Midpoint of the Interval
How to Make a Box Plot From a Cumulative Frequency
How to Find Correlation Coefficient & Coefficient of...
How to Calculate the Area Under a Normal Curve
How to Write an Equation for a Function
How to Determine the Bin Width for a Histogram
How to Calculate Correlation Coefficient Between Two...
How to Make a Coordinate Plane in MS Excel
How to Do an Absolute Value Function on the TI-83 Plus
How to Solve a Matrix
How to Differentiate a Function
How to Solve 3-Variable Linear Equations on a TI-84
How to Find Equations of Tangent Lines
How to Graph a Function

Dont Go!

We Have More Great Sciencing Articles!