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Activities 71
Demonstrating the Fundamental Theorem of
Calculus
Problem 1
Using the functions fnInt( and nDeriv( from 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 1àT 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 1àX and the function 1àX. Set the graph style for
Y3 to ç (line) and Y4 to è (thick).
Xmin=.01
Xmax=10
Xscl=1
Ymin=
L1.5
Ymax=2.5
Yscl=1
Xres=3
Fx() td
1
x
∫
x() x 0>,ln==
Dx
1
t
---
td
1
x
∫
1
x
---=