AP Calculus

Special Focus: The Fundamental
Theorem of Calculus
Note that there will be one entry fewer in L5 than in L1, L2, L3, or L4. To compensate,
you can enter one additional value at the end of L5 “by hand.” In the Stat Editor, position
the cursor in L5(48) (one cell past the last entry), press Enter, and enter the expression
(Y2(4.8)-Y2(4.7))/0.1. This will even out the lists. Define PLOT3 as L5 versus
L1. In addition, deselect PLOT1 and PLOT2. See the screen shots below.
If you fail to do this correctly, you will probably get the error DIM MISMATCH, telling
you the lengths of the lists you are trying to graph don’t match. If this happens, fix the
lists so they have the same length.
Note: It may be necessary to execute the SetUpEditor command in order to see L5.
On the HOME screen, select 5:SetUpEditor from the STAT menu and press ENTER.
Finally, change the style of the graph of Y1 from the Y= editor by positioning the cursor
to the left of Y1 and repeatedly pressing the ENTER key until the style shown resembles a
circle with a little tail. That way, you’ll be able to see the graph of Y1 running overtop of
the scatterplot. See the screen shots below.
Cool! What you just did was calculate 47 difference quotients for the function Y2. Each
difference quotient value in the list L5 approximates the derivative of Y2. You then
graphed the integrand on top of the scatterplot of those 47 difference quotients and
saw the graphs coincide. This provides more evidence in support of the Fundamental
Theorem of Calculus.
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AP® Calculus: 2006–2007 Workshop Materials