Evaluating A Definite Integral From The Graphics Screen - Texas Instruments TI-84 Plus Manual

Because part a of Example 3 asks for the areas of the regions
above and below the input axis and the function, we must find
where the function crosses the axis.
You can find this value using the solver (solve
using the graph and the x-intercept method described on page
A-11 of this guide.
CAUTION: If you round the x-intercept value, it will cause whatever you do with this value
to not give as an accurate result as possible. This situation occurs many times in this and the
next several chapters of the text. Also recall that one of the numerical considerations given in
Chapter 1 of Calculus Concepts is that intermediate calculation values should not be rounded.
For maximum accuracy, store this value in some memory location, say
all subsequent calculations.
Whether you use the
on the calculator screen above, the calculator stores the value
for the x-intercept in
Return to the home screen and store the value in
memory location, except
location because the
calculator table, the solver, or trace a graph. Type
ALPHA 2.
Find the area of the region above the horizontal axis by typing
and entering the first expression shown on the right.
Find the area of the region below the horizontal axis by typing
and entering the second expression shown on the right. (The
negative is used because the region is below the input axis.)
Part b of Example 3 asks you to evaluate
value by typing and entering the expression shown on the right.
Note that the result is not the sum of the two areas – it is their
difference.
•
If you evaluate a definite integral using antiderivative formulas and check your answer with
the calculator using
Remember that the calculator is evaluating the definite integral using an approximation
technique, not an algebraic formula.

EVALUATING A DEFINITE INTEGRAL FROM THE GRAPHICS SCREEN

value of a definite integral can also be found from the graphics screen. We again illustrate the
use of with the function that models the rate of change of the average sea level.
fnInt
Turn off
Plot 1
level in . (See page 69 of this Guide.) We want to evaluate
Y1
z
0
.
Y1
dx
−
7
76
or the x-intercept method shown
SOLVER
.
X
, that you choose). Do not use the
X
value changes whenever you use the
X
, you might find a slight difference in the last few decimal places.
fnInt
and have the function modeling the average sea
= 0) or by
Y1
(or whatever
Z
X
with
Z
z
0
. Find this
Y1
dx
−
7
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Chapter 5
, and refer to it as in
Z Z
The