Please notice that functions SIGMAVX and SIGMA are designed for
integrands that involve some sort of integer function like the factorial (!)
function shown above. Their result is the so-called discrete derivative, i.e.,
one defined for integer numbers only.
In a definite integral of a function, the resulting anti-derivative is evaluated at
the upper and lower limit of an interval (a,b) and the evaluated values
where f(x) = dF/dx.
The PREVAL(f(x),a,b) function of the CAS can simplify such calculation by
returning f(b)-f(a) with x being the CAS variable VX.
To calculate definite integrals the calculator also provides the integral symbol
as the keystroke combination ‚Á (associated with the U key). The
simplest way to build an integral is by using the Equation Writer (see Chapter
2 for an example). Within the Equation Writer, the symbol ‚Á
produces the integral sign and provides placeholders for the integration limits
(a,b), for the function, f(x), and for the variable of integration (x). The
following screen shots show how to build a particular integral. The insert
cursor is first located in the lower limit of integration, enter a value and press
the right-arrow key (™) to move to the upper limit of integration. Enter a
value in that location and press ™ again to move to the integrand location.
Type the integrand expression, and press once more to move to the
differential place holder, type the variable of integration in that location and
the integral is ready to be calculated.