Texas Instruments TI-83 Demonstrating the Fundamental Theorem of Calculus

17-14 Applications

8317APPS.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:00 PM Printed: 02/19/01 1:39 PM

Page 14 of 20

Using the functions fnInt( and nDeriv( from the MATH menu

to graph functions defined by integrals and derivatives

demonstrates graphically that:

F(x) = ‰1

1àt dt = ln(x), x > 0 and that

Dx[‰1

1àt dt] = 1àx

1. Press z. Select the default settings.

2. Press p. Set the viewing window.

Xmin=.01 Ymin=M1.5 Xres=3

Xmax=10 Ymax=2.5

Xscl=1 Yscl=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 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).

6. Press r. Again, use the cursor keys to compare the

values of the two graphed functions, Y3 and Y4.

Demonstrating the Fundamental Theorem of Calculus

Problem 1

Procedure 1