Chapter 17: Activities
319
Demonstrating the Fundamental Theorem of Calculus
Problem 1
Using the functions
fnInt(
and
nDeriv(
from the
FUNC
shortcut menu or the
MATH
menu to graph
functions defined by integrals and derivatives demonstrates graphically that:
and that
Procedure 1
1. Press
z
. Select the default settings.
2. Press
p
. Set the viewing window.
3. Press
o
. Turn off all functions and stat plots. Enter the numerical integral of 1
à
T from 1 to X
and the function ln(X). Set the graph style for
Y1
to
ç
(line) and
Y2
to
ë
(path).
4. Press
r
. Press
|
,
}
,
~
, and
†
to compare the values of
Y1
and
Y2
.
5. Press
o
. Turn off
Y1
and
Y2
, and then enter the numerical derivative of the integral of 1
à
X
and the function 1
à
X. Set the graph style for
Y3
to
ç
(line) and
Y4
to
è
(thick).
Xmin=.01
Xmax=10
Xscl=1
Ymin=
L
1.5
Ymax=2.5
Yscl=1
Xres=3
