*Simon Woodhead writes:*

**Floor and ceiling functions** are not available in the current version of **Autograph**, but will be in a future version. The** y = int(x)** function is actually a truncation function so int(-3.2) = -3 and int(3.2) = 3. This is not the most useful function, but can be used to define ceiling and floor functions.

Open a 2D graph page and click on Function Definitions. Define:

** f(x) = ((int(x) + |int(x)|) + (int(x − 1) − |int(x − 1)|))/2**

** g (x) = f(x) + 1**

Then f(x) is the **floor function** and g(x) is the **ceiling function**.

First import the image, and enter lots of points along the top edge.

Select a group of points that you think could be modelled by a polynomial and use the “best Fit” option. The default ‘sig’ fig’ is 4, but a polynomial equation needs more accuracy to plot accurately. Use “PAGE – SETTINGS” to set the sig fig to 8. With the current best fit selected, use the PAGE menu and the option “Copy Status Bar”, and in a 3D page use “Enter equation” and paste this in, with “Plot as 2D” ticked, and Startup Options set to the domain.

In the 3D page, select each sector, use “Find Area” with “Simpson’s Rule” selected, then “Volume” about y = 0.