Demonstrating The Fundamental Theorem Of Calculus - Texas Instruments TI-82 STATS Manual Book

Demonstrating the Fundamental Theorem of Calculus

Problem 1
Procedure 1
17–14 Applications
Using the functions
graph functions defined by integrals and derivatives
demonstrates graphically that:
x
‰
F(x) = 1àt dt = ln(x), x > 0 and that
1
x
[‰ ]
D 1àt dt = 1àx
x
1
1. Press z. Select the default settings.
2. Press p. Set the viewing window.
Xmin=.01
Xmax=10
Xscl=1
3. Press o. Turn off all functions and stat plots. Enter the
numerical integral of 1àT from 1 to X and the function
ln(X). Set the graph style for
ë (path).
4. Press r. Press |, }, ~, and † to compare the values
of and .
Y Y
1 2
5. Press o. Turn off
derivative of the integral of 1àX and the function 1àX. Set
the graph style for
6. Press r. Again, use the cursor keys to compare the
values of the two graphed functions,
and from the
fnInt( nDeriv(
Ymin=M1.5
Ymax=2.5
Yscl=1
to ç (line) and
Y
1
and , and then enter the numerical
Y Y
1 2
ç ç ç ç
to (line) and
Y
3
menu to
MATH
Xres=3
to
Y
2
è è è è
to (thick).
Y
4
and .
Y Y
3 4