User Guide

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 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 1
àX. 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