Operation Manual

14-18 Applications
8214APPS.DOC TI-82, Chapter 14, English Bob Fedorisko Revised: 02/09/01 9:27 AM Printed:
02/09/01 12:43 PM Page 18 of 20
Fundamental Theorem of Calculus
The TI
.
82 can graph functions that are defined by integrals or derivatives, using
the functions fnInt( and nDeriv( from the MATH MATH menu.
Problem 1
Demonstrate graphically that
F(x) =
‰
1
x
1
à
t dt = ln(x), x>0 and that
D
x
[
‰
1
x
1
à
t dt ] = 1
à
x
Procedure 1
1. Press
z
. Select
Simul
and the default
MODE
settings. Press
o
and
turn off all functions. Press
y
[
STAT PLOT
] and turn off all stat plots.
2. Press
p
. Set the viewing
WINDOW
.
Xmin = .01 Ymin =
M
1.5
Xmax = 10 Ymax = 2.5
Xscl = 1 Yscl = 1
3. Press
o
. Enter the numerical integral of 1
à
T and the mathematical
integral of 1
à
X.
Y
1
=fnInt(1
à
T,T,1,X)
Y
2
=ln X
4. Press
r
. The busy indicator displays while the graph is being
plotted. Use the cursor keys to compare the values of
Y
1
and
Y
2
.
5. Press
o
. Turn off
Y
1
and
Y
2
, and then enter the numerical derivative of
the integral of 1
à
X and the function 1
à
X.
Y
3
=nDeriv(Y
1
,X,X)
Y
4
=1
à
X
6. Press
r
. The busy indicator displays while the graph is being
plotted. Again, use the cursor keys to compare the values of the two
graphed functions,
Y
3
and
Y
4
.