Texas Instruments TI Programmable 57 User Manual

EVALUATING INTEGRALS:
SIMPSON'S RULE
As
an
example,
we'll
write
a
program
for
(and
evaluate)
the
integral
of
y
—
2x?
+
3x
—
1
froma
=
1
tob
=
5,
usingn
=
6.
(Note,
the
integral
approximation
gets
more
accurate
as
n
is
made
larger.)
DESTINATION
We'll
construct
a
program
with
a
subroutine
that
repeatedly
solves
the
equation
y
=
2x?
+
3x
—
1,
for
each
value
of
x
between
a
and
b.
Then
using
these
values
Simpson's
approximation
will
be
computed.
The
program
will
be
constructed
so
that
you'll:
Enter
n
(number
of
divisions
—
must
be
an
even
integer).
and press 0.
+ Enter b and press 1.
Enter a and press [S1} 2.
:
Press
,
and
atter
a
wait,
the
display
will
read
the
integral
of
the
function.
To
evaluate
the
integral
of
any
new
function
all
that
must
be
altered
will
be
subroutine
1,
which
evaluates
the
function.
Just
press
1
while
out
of
LEARN
mode,
press
,
enter
the
new
function
(remembering
that
x
is
in
memory
2)
and
end
with
an.
[iN]
,
Press
again,
enter
your
new
values
for
a,
b,
and
nand
continue.
PLANNING THE Route
Since
y
=
f(x)
=
2x?
+
3x
—
1
needs
to
be
evaluated
many
times
in
this
program,
and
needs
to
be
easily
changeable
so
that
other
integrals
can
be
evaluated,
we'll
place
it
in
a
subroutine
at
the
end
of
the
program.
We'll
begin
the
program
by
calculating
w
=
",
storing
it
and
recalling
as
we
need
it.
We'll
include
program
steps
to
find
the
right
multiplying
number
(called
coefficients)
for
each
“Y’’
term
in
the
Simpson's
rule
formula:
Area
=a
+4Y,
+
2Y,
+
4¥,
+...
+
2Y,_,+4Y,
+Y,,,)-
(Note
that
the
coefficients
of
Y
will
either
be
1,
2,
or
4
depending
on
which
term
we're
evaluating.)
We'll
use
subroutine
|
to
evaluate
each
Y
term,
multiply
by
the
correct
coefficient
and
sum
the
result
to
memory
3.
Then
we'll
step
to
the
next
x
value,
determine
a
new
coefficient,
a
new
Y
value,
and
repeat
for
n
steps.
At
the
end
of
these
steps,
we'll
compute
Y,,.,,
sum
it
to
3,
multiply
by
¥
and
display
the
final
result.

Texas Instruments TI Programmable 57 Specifications

General

Brand	Texas Instruments
Model	TI Programmable 57
Category	Calculator
Language	English