Since one can not look the result of the published notebooks, I use its code to playing around a little bit, so here are the plots.
The default function to be integrated is , the interval of integration is set , the number of partitions of the interval is 4, and the method is the mid-point,
We can see the visual integration, the analitic result, the numerical one, and the error. 🙂 Nice, Isn’t it?
Let’s change the number of partitions, say to 10,
Much better! But now, let’s try the other methods… left-point,
The trapezoid method,
which is one of the best.
But finally the Simpson method,
So, I think it’s a good idea to give a try to the interactive mode in SAGE, and if you go thru the code you’ll find out it’s not as difficult as it seems.