Press the GRAPH key and the graph will appear.
The Program NINT
NINT finds a numerical approximation to
Z
b
a
f(x) dx.
Use NINT to find an approximation to
Z
2
1
4x
3
dx.
(This is Exercise 1 in Section 6.5 of the text.)
Solution. We wish to evaluate
Z
2
1
4x
3
dx. Press the
following keys
MATH 9 4 X,T,θ ∧ 3
,
X,T,θ
,
1
,
2 ) ENTER
You will see
The answer is 15.
Section 7.3 in Text
• The Program TRAP
• The Program SIMP
The Programs TRAP and SIMP
Use the programs TRAP and SIMP to find
the trapezoidal and Simpson approximation for
Z
2
0
p
4 − x
2
dx = π for n = 100, 200, 400. Compare
the results. (Refer to Example 4 in the text.)
Solution. First input Y
1
=
√
4 − x
2
. Execute the pro-
gram TRAP. A lower limit (of integration) is requested.
Press the keys
0 ENTER . An upper limit (of inte-
gration) is requested. Press the keys 2 ENTER . The
value of N is requested. Press 1 0 0 . Wait about
15 seconds and you see
T=
3.140417032
Done
Press ENTER to start the program again.
The program SIMP works in a similar manner.
Section 8.6 in Text
The Program VOL
Find the Riemann sums for the functions f(x, y) =
6xy
2
using the domain consisting of the rectangle R =
{(x, y) : 0 ≤ x ≤ 2, 0 ≤ y ≤ 1}, for n = 4, 8, and 100
by taking the points (x
i
, y
i
) at the lower left and then
the top right of each subrectangle. (Refer to the table
in Section 8.6.)
Solution. Execute the program VOL. The program is
set to use the domain R = {(x, y) : A ≤ x ≤ B, C ≤
y ≤ D}. Therefore, when requested set A = 0, B = 2,
C = 0, and D = 1. The program then request N .
Select an N . The calculator will need to run many
minutes for N = 100.
Section 9.2 in Text
Reproduce Screen 9.1 in the Text
Solution. Set the mode functions to radian, para-
metric, and simultaneous. Set the range variables to
T
min
= 0, T
max
= 6.28, T
step
= 0.01. Use a view-
ing window with dimensions [−1, 6.26] by [−2, 2]. Set
x
1
= cos t, y
1
= sin t (giving the unit circle), and
x
2
= t, y
2
= sin t, and graph. As the graph slowly
46
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