HP 48g Graphing Calculator - Manual (Page 242)

......................... INTEGRATE j
EKPR:
VAR: LQ:
RESULT: Humeric
NUMBER FURMAT:
Std
ENTER EKPRESSI0N
The Numeric INTEGRATE Screen.
20
(5. Set the number display format to indicate the accuracy factor you
desire for the computation. The Std format yields the highest
accuracy factor (and consequently the longest calculation time)
while Fix 0 (or Sci 0 or Eng 0) yields the lowest accuracy factor
(and the shortest calculation time). See “The Accuracy Factor and
the Uncertainty of Numerical Jntegration” on page 20'^6.
7. Press OK to compute the integral.
Improper integrals are those integrals where one or both limits are
infinity (oc). The HP 48 is a calculator with finite computational
limits and thus must always use finite limits when computing numeric
integrals. However, b}' using a transformation of variables, jmu can
map an unbounded domain onto a bounded one.
One useful transformation, y = arctan
x,
maps the entire real ,r-axis
onto the bounded interval ^ < y < f ■ This is the transformation:
f(x)dx
ar eta 7100= ^
a7'ctan—co= -
/(tan ij) • (1 + tan ''y)dy
To evaluate an improper integral:
1. Make sure that you are in Radian mode (press RAD), if
necessary).
2. Press fr^fSYMBOLIC 1 OK to open the ! form.
3. Enter the integrand from tl«' improper integral into the ExF'FOi
field.
4. With the Ex field highlighted, press f NXT ) CFlLC and enter
the transformation expression onto the stack. For example, if the
variable of integration for the improper integral is x. you would
enter TflNCf) to make the transformation {x = tan y) shown
above. Make a extra copy of transformation expression by pressing
( e n t e r )
a second time.
20-2 Calculus and Symbolic Manipulation