Texas Instruments TI-82

34
G
RAPHING
T
ECHNOLOGY
G
UIDE
: TI-82
Copyright © Houghton Mifflin Company. All rights reserved.
Figure 2.85: Newton’s method
Technology Tip: Newton’s Method is sensitive to your seed value for x, so look carefully at the function’s graph to
make a good first estimate. Also, remember that the method sometimes fails to converge!
You may want to save the Newton’s Method formula as a short program. See your calculator’s manual for further
information on programming the TI-82.
2.12 Integration
2.12.1 Approximating Definite Integrals: The TI-82 has the function fnInt( in the MATH menu to approximate an
integral. So to find a numerical approximation to
1
0
cos
∫
x
2
dx with a tolerance of 0.001 (which controls the accuracy
of the approximation), press MATH 9 COS
X,T,θ
x
2
,
X,T,θ
, 0 , 1 , .001 ) ENTER as shown in Figure 2.86. The
format of this command is fnInt(expression, variable, lower limit, upper limit, tolerance). The same integral is
also approximated in Figure 2.86 using a tolerance of 0.00001, the TI-82’s default that is used when no other
tolerance is specified.
Figure 2.86 fnlnt(
2.12.2 Areas: You may approximate the area under the graph of a function y =f (x) between x = A and x = B with
your TI-82. For example, here are keystrokes for finding the area under the graph of the function y = cos x
2
between
x = 0 and x = 1. This area is represented by the definite integral
1
0
cos
∫
x
2
dx. So graph f (x) = cos x
2
and press 2nd
CALC 7. Use the arrow keys to trace along the curve to the lower limit and press ENTER; then trace again to the
upper limit (see Figure 2.87) and press ENTER. The region under the graph between the lower limit and the upper
limit is shaded and the area is displayed as in Figure 2.88. The TI-82 uses fnInt( with the default tolerance of 10
-5
in
this calculation.