Suppose you want to integrate f(x) from x1 to x2;   g = integral f dx, and f = dg/dx .  Revised 8/10/02

Open a blank worksheet and in cell A1 type Integral.xls as the name of the worksheet.

Save the worksheet someplace as Integral.xls.

[In what follows, column C is actually superfluous.
We don't need dg/dx at the full step, only at the half-step.]

In cell A3 type f = 3 x^2  (This is just text to let you know what you are integrating)

In cell A4 type Steps.     In cell A5 type x1      In cell A6 type x2
In cell A7 type x step     In cell A8 type half step, In cell A9 type Integral

Now name the various cells.  This makes it easier to refer to the cells, and gives them an absolute address.
Select cell B4. Under Insert/Name/Define it will show Steps; click OK unless you want a different name.

Select cell B5. When you go to select x1 as a name it says it is illegal. Change it to x_1 and it will like it.
Ditto for cell B6. For cell B7 it will put in an underscore and prompt you with x_step. Same for cell B8.

Now for values in the cells. In Steps (B4), put 100, in x_1 (B5) put 0, in x_2 (B6) put 2, in x_step (B7) put =(x_2-x_1)/Steps
In half_step (B8) put =x_step/2 .

Now set up the numerical integration.
(RK2 requires derivatives to be evaluated at the half-step, and then bringing the values forward a full step using the half-step derivatives.)

In cell A11 type Full Step, in A12 type x, in B12 type g, in C12 type dg/dx.
In cell D11 type Half Step, in D12 type x, and in E12 type dg/dx

In cell A13, type 0, in cell B13 type 0, in cell C13 type =3*A13^2, in cell D13 type =A13+half_step, and in E13 type =3*D13^2.

In cell A14 type =A13+x_step, in cell B14 type =B13+x_step*E13.
Select cells C13 through E13 and copy them down into cells C14..E14.

Select cells A14..E14. Copy them down through cells A113..E113

In cell B9 type =B113 .   This is the value of the integral between the limits x1 and x2.