Datasheet

81
Integration: The algebraic indefinite integral
Algebraic integration is also possible (for simple functions), in the following
fashions:
i. If done in the SYMB view of the Function aplet, then the integration
must be done using the symbolic variable S1 (or S2, S3, S4 or S5). If
done in this manner then the results are very good, except that there is
no constant of integration ‘c’.
The screenshot right shows the results of
defining
2
1( ) 1FX X
=
− and then
()
2
2( ) 0, 1, 1,FX SX X=−
∫
, together with
the results of the same thing after
pressing the key (the result is placed
in F3 only for convenience of viewing). All
that is now necessary is to read ‘-S1+S1^3/3’ as
3
3
x
x−+ , or as it
should be read as
3
3
x
x
c−+ .
ii. If done in the HOME view, then S1 must
again be used as the variable of
integration.
i.e.
2
1
x
dx−
∫
is entered as
∫
( 1, S1, X
2
- 1, X ).
This is shown right, together with the results of highlighting the answer
and pressing
. The calculator assumes that X itself may be a
function of some other variable and integrates accordingly as a ‘partial
integration’ which, while mathematically correct, is not what most of us
want.
The way to simplify this answer to a
better form is to highlight it, it, and
press ENTER again, giving the result
shown right. This is the result of the
calculator performing the substitutions
implied in the previous expression.