Examples Workbook

Computing Multiple Integrals in Excel

QUADF can be nested to compute multiple integrals of any order. This allows for individualized control of each nested integral such as algorithm selection. To illustrate the process consider a volume integral:

$$\underset{a}{\overset{b}{\int }}\underset{l_y\left(x\right)}{\overset{u_y\left(x\right)}{\int }}\underset{l_z(x,y)}{\overset{u_z(x,y)}{\int }}f\left(x,y,z\right) dzdydx$$

The general steps required to perform the above integral are as follows:

1. Select variables of integration. For example X1, Y1, Z1 and define formulas for the integrand f(x,y,z), and the limits functions l_z(x,y), l_y(x), u_z(x,y), and u_y(x,y) in terms of the selected variables. You may also pass expressions for limits functions directly into the parameters for QUADF formulas as shown in the examples.

2. In a cell (e.g., A1) enter QUADF formula for the inner most integral.

3. In a second cell (e.g., A2) enter QUADF formula for the middle integral and specify A1 for the integrand.

4. In a third cell (e.g., A3) enter QUADF formula for the outer integral and specify A2 for the integrand. Evaluate A3 to compute the triple integral.