Texas Instruments TI Programmable 57 User Manual

If
you've
had
any
calculus
courses,
you're
probably
familiar
with
the
integral
symbol]
'/"’.
This
symbol
stands
for
“the
integral
of'’and
a/"
4(x)dx
is
read
"the
integral
of
f(x)
from
a
to
b
—
and
represents
the
area
under
the
curve
y
=
{(x)
from
point.a
to
point
b
as
shown
in
the
figure.
If you know the techniques of
integral calculus, you know that
there are methods allowing you to
evaluate this integral exactly. You
also know that in some cases this
evaluation may be extremely
difficult; or even impossible!
In these cases, approximation
techniques are sometimes used
One of these approximation methods
is called Simpson's approximation.
When using Simpson's
approximation (or Simpson's rule,
as it's often called), you divide the
area under the curve into an even
number of parts (n). The width of
each part, w, is then given by:
w = In the figure shown, we've
divided the area into 6 parts, so
w = 4+ To compute the
approximate total area under the
curve (the approximate value of
the integral), you use the following
formula: a
Area
=
F
X
(¥,
+/4Y+
2Y,
+
4¥,
+
....
+
2¥,_,
+
AY
+
Yoo
This
formidable
looking
formula
is
actually
quite
easy
to
evaluate
with
the
program
we'll
develop
in this
section.
Y
M X, My KX HX Me x x
b
Here Y, = the Y value withx = a
Y, = the Y value withx = a +.w
Y, = the Y value with x = a + w + w,
etc.
Yas. = the Y value with x = b

Texas Instruments TI Programmable 57 Specifications

General

Brand	Texas Instruments
Model	TI Programmable 57
Category	Calculator
Language	English