One of the topics that are studied in a first course in integral calculus is
the process of approximating a given integral 
by various types of sums. In studying this topic, we are not just concerned
with the act of finding approximations to the integral. An approximate value
of an integral can be obtained by a single click on Evaluate
Numerically with SWP. The purpose of this topic is to acquaint
students with a variety of different kinds of sums such as left sums, right sums, trapezoidal sums, midpoint sums and
Simpson sums, to point out that some of these sums will approximate
a given integral more closely than others and to show that all of them
provide better approximations when the interval of integration is more
finely partitioned. We would like to know how much better the better sums
are and how much better the sums become when the interval is more finely
partitioned.
In this example, we shall show how Scientific WorkPlace can be
used to study the left sums, right sums, trapezoidal sums, midpoint sums and
Simpson sums of a given function f on an interval 
and
how a course in integral calculus can thus be enriched with the help of
Scientific WorkPlace.