281
Prgm: INTEGRAL Where to Find The Commands
:Disp “LOWER LIMIT” Disp and Input are accessed via PRGM, I/O
:Input
A
Enter lower limit of integration.
:Disp “UPPER LIMIT”
:Input
B
Enter upper limit of integration.
:Disp “DIVNS”
:Input
N
Enter number subdivisions.
:
(
B
,
A
)
=N
!
H
Stores size of one subdivision in
H
(Note that
!
means
hit STO button).
:
A
!
X
Start
X
off at beginning of interval.
:0
!
L
Initialize
L
, which keeps track of left sums, to zero.
:0
!
M
Initialize
M
, which keeps track of midpointsums, to zero.
:1
!
I
Initialize
I
, the counter for the loop.
:Lbl P Label for top of loop. Lbl is accessed via PRGM, CTL.
:
L
+
H
Y
1
!
L
Increment
L
by
Y
1
H
, the area of one more rectangle.
(
Y
1is accessed via
Y
-VARS, or 2nd VARS.)
:
X
+
:
5
H
!
X
Move
X
to middle of interval.
:
M
+
H
Y
1
!
M
Evaluate
Y
1at the middle of int erval and increment
M
by rectangle of this height.
:
X
+
:
5
H
!
X
Move
X
tostartofnextinterval.
:
IS >
(
I;N
)
IS >
(
is accessed via PRGM, CTL. This is the most
difficult step in the program: adds 1 to
I
and does the
the next step if
I
N
(i.e., if haven’t gone through
loop enought times); otherwise, skips next step. Thus,
if
I
N
, goes back toLbl P and loops throughagain.
If
I>N
, loop is finished and goes on to print out
results. Continue here if
I>N
, in which case
the value of
X
is now
B
.
:Goto P Goto is accessed vi a PRGM, CTL. Jumps back to
Lbl P if
J
N
.
:Disp “LEFT/RIGHT”
:Disp
L L
now equals the left sum, so display it.
:
L
+
H
Y
1
!
R
Add on area of right-most rectangle, store in
R
.
:
A
!
X
Reset
X
to
A
.
:
R
,
H
Y
1
!
R
Subtract off area of left-most rectangle.
:Disp
R R
now equals right sum, so display it.
:
(
L
+
R
)
=
2
!
T
Trap approximation is average of
L
and
R
.
:Disp “TRAP/MID/SIMP”
:Disp
T
Display trap approximation.
:Disp
M
Display midpoint approximation.
:
(
2
M
+
T
)
=
3
!
S
Simpson is weighted average of
M
and
T
.
:Disp
S
Display Simpson’s approximation.
