The Definite Integral; Evaluating A Definite Integral On The Home Screen - Texas Instruments TI-84 Plus Manual

TI-83, TI-83 Plus, TI-84 Plus Guide
Enter f in ,
Y1
, using a different number for C in each function location.
Y6
(You can use the values of C shown to the right or different
values.)
Find a suitable viewing window and graph the functions
through . The graph to the right was drawn with
Y6
− 20 ≤ y ≤ 20.
and
It appears that the only difference in the graphs of
is the y-axis intercept. But, isn't C the y-axis intercept of each of
these antiderivative graphs?
Clear
Y4, Y5,
Press
GRAPH
see only one graph.
Set the calculator
appears that
Y2
CAUTION: The methods for checking derivative formulas that were discussed in Sections
4.3.2b and 4.3.2c are not valid for checking general antiderivative formulas. Why not? Because
to graph an antiderivative using
integration and for the input of the lower endpoint. However, for most of the rate-of-change
functions where f(0) = 0, the calculator's numerical integrator values and your antiderivative
formula values should differ by the same constant at every input value where they are defined.

5.4 The Definite Integral

When using the numerical integrator on the home screen, enter
function f with input x and specific values of a and b. (Remember that the input variable does
not have to be x when the function formula is entered on the home screen.) If you prefer, f can
be in the list and referred to as
Y=

EVALUATING A DEFINITE INTEGRAL ON THE HOME SCREEN

use of with the function that models the rate of change of the average sea level. The rate-
fnInt
of-change data are given in Table 6.18 of Example 3 in Section 5.4 of Calculus Concepts.
Time
(thousands of years before the present)
Rate of change of average sea level
(meters/year)
Enter the time values in
sea level values in
quadratic function. Find the function and paste it in
(Draw the function on the scatter plot of the data to confirm that
it gives a good fit.)
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in , and F in
fnInt(Y1, X, 0, X) Y2
and Turn off and change the
Y6. Y1
and draw the graphs of
to and enter some values for x. It
TABLE ASK
and are the same function.
Y3
, you must arbitrarily choose values for the constant of
fnInt
(or whatever location is chosen) when using
Y1
and the rate of change of the average
L1
. A scatter plot of the data indicates a
L2
, , , and
Y3 Y4 Y5
Y1
− 3 ≤ x ≤ 3
through
Y2 Y6
in to .
1 Y3 0
and . You should
Y2 Y3
fnInt(f(x), x, a, b)
− − −
7 6 5
3.8 2.6 1.0
.
Y1
for a specific
fnInt.
We illustrate the
− − − −
4 3 2 1
0.1 − − −
0.6 0.9 1.0
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