Double Integration Examples

On this webpage, we provide examples of how to use the Real Statistics INTEGRAL2 worksheet function (see Numerical Double Integration) to perform double integration in Excel.

Examples (numerical limits)

Example 1: Evaluate

Example 1

As you learn in calculus

Example 1 evaluation 1

Example 1 evaluation 2

Instead, we can use the Real Statistics INTEGRAL2 function as shown in cell B10 of Figure 1.

Example 1 using INTEGRAL2

Figure 1 – INTEGRAL2 with finite limits

Cells B12, B13, and B13 show alternative ways of specifying the formula using the Real Statistics LAMB function.

Cell B16 shows that

Inverting x and y

as expected since the value of the double integral should be the same even if you interchange the roles of x and y.

Examples (function limits)

Example 2: Evaluate

Functional limits example

By calculus

Example 2 analysis 1

Example 2 analysis 2

We obtain a similar result by using INTEGRAL2, as shown in cell G10 of Figure 2.

Using INTEGRAL2 function

Figure 2 – INTEGRAL2 with function limit

The approach is similar to that shown in Figure 1, except that this time the upper limit for x (cell G6) is specified by a formula (as shown in cell H6).

Examples (infinite limits)

Example 3: Evaluate

Improper double integral example

By calculus

Example 3 analysis 1

Example 3 analysis 2

Once again, we obtain a similar result by using INTEGRAL2, as shown in cell L10 of Figure 3.

Using INTEGRAL2 function

Figure 3 – INTEGRAL2 with infinity limit

Examples Workbook

Click here to download the Excel workbook with the examples described on this webpage.

Reference

Mahaffy, J. (2010) Numerical integration and differentiation – multiple integrals; improper integrals
https://jmahaffy.sdsu.edu/courses/s10/math541/lectures/pdf/week09/lecture.pdf

Leave a Comment