and ENTER . A graph of y = x
2
appears on the in-
terval [0, 1] together with the rectangles associated with
the right-hand sums.
Press ENTER and the value of the right-hand sum
is given. Press
ENTER and a graph of y = x
2
ap-
pears on the interval [0, 1] together with the rectangles
associated with the left-hand sums.
Press ENTER and the value of the left- and righthand
sums is given.
Press ENTER again and another n is requested, and
so on.
The Program SUM
The program SUM finds the left- and right-hand sums,
but does not draw the rectangles as done in the program
RECT. Use the program SUM to find the left and right-
hand sums for
Z
1
0
x
2
dx when n = 50.
Solution. First input Y
1
= x
2
. Execute the program
SUM. A lower limit (of integration) is requested. Press
the 0 key and the ENTER key. An upper limit (of
integration) is requested. Press the 1 key and the
ENTER key. Now N is requested. Press the keys 5
0 ENTER . Wait several seconds and you then see
Pressing ENTER will start the program again.
Section 6.5 in Text
• NINTG
• NINT
The Program NINTG
The program NINTG graphs a numerical approxima-
tion to the integral
Z
x
a
f(x) dx on a prescribed interval.
Use NINTG to graph an approximation to
Z
x
0
t
2
dt.
Solution. First set the dimensions of the view-
ing window to [−2, 2] by [−3, 3]. On the TI-
82 NINTG is a built-in function. Use the func-
tion fnInt(. This function requires you to fill in
fnInt(expression,variable,lower,upper). So press the
keys
Y = MATH 9 X,T,θ ∧ 2
,
X,T,θ
,
0
,
X,T,θ )
You will see the following.
45
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