Demonstrating The Fundamental Theorem Of Calculus - Texas Instruments TI-84 Plus Manual Book

Demonstrating the Fundamental Theorem of
Calculus
Problem 1
Using the functions
functions defined by integrals and derivatives demonstrates graphically
that:
x
∫
F x ( )
=
1
x
1
∫
-- - t d
Dx
t
1
Procedure 1
Press z. Select the default settings.
1.
Press p. Set the viewing window.
2.
Xmin=.01
Xmax=10
Xscl=1
Press o. Turn off all functions and stat plots. Enter the numerical
3.
integral of 1àT from 1 to X and the function ln(X). Set the graph style
to ç (line) and
for
Y1
Press r. Press |, }, ~, and † to compare the values of
4.
.
Y2
Press o. Turn off
5.
of the integral of 1àX and the function 1àX. Set the graph style for
to ç (line) and
Y3
Activities
and
fnInt( nDeriv(
x ( ) x 0 >
t d = ln ,
1
=
-- -
x
L
Ymin=
Ymax=2.5
Yscl=1
to ë (path).
Y2
and
Y1 Y2
to è (thick).
Y4
from the
and that
Xres=3
1.5
, and then enter the numerical derivative
menu to graph
MATH
and
Y1
87