Area Approximations Using Right Rectangles; Area Approximations Using Midpoint Rectangles - Texas Instruments TI-84 Plus Manual

TI-83, TI-83 Plus, TI-84 Plus Guide
AREA APPROXIMATIONS USING RIGHT RECTANGLES We continue with the
previous function and find an area approximation using right rectangles.
Part a of Example 2 says to find the change in the drug concen-
tration from x = 0 through x = 20 using right rectangles of width
2 days. Enter the right endpoints
Use the piecewise continuous function r in
find the rectangle heights. As shown, enter the heights in
•
Note that the heights in
values have been rounded for printing purposes.
Find the right-rectangle areas by multiplying each entry in
by 2. This is the same as multiplying the sum of the heights by
2. On the home screen, press
► [MATH] 5 [sum] 2ND 2 (L2) )
Part b of Example 2 asks us to use the model and right rectangles of width 2 days to estimate
the change in drug concentration from x = 20 to x = 30. Notice that the signed heights in
are the same as those given in the text in Table 5.4 (except for rounding.)
Enter the right endpoints
Use the piecewise continuous function r in
find the rectangle heights. As shown to the right, enter the
signed heights in
Find the signed right-rectangle areas by multiplying each entry
in by 2. This is the same as multiplying the sum of the signed
L2
heights by 2. On the home screen, press
to return the sum instruction to the screen, change
(ENTRY)
with
L4 ◄ ◄
AREA APPROXIMATIONS USING MIDPOINT RECTANGLES Areas of midpoint
rectangles are found using the same procedures as those used to find left and right rectangle
areas except that the midpoint of the base of each rectangle is entered in the first list and no
endpoints are deleted. We illustrate the midpoint-rectangle approximation using the function f
in Example 3 of Section 5.1 in Calculus Concepts.
Clear all functions from the
2
f (x) = −
4 x
(Type the square root symbol with
Copyright © Houghton Mifflin Company. All rights reserved.
(2, 4, 6, ..., 20)
are the values in Table 5.3 in the text, but the Table 5.3
L2
2 2ND
(22, 24, 26, 28, 30)
.
L4
and then type
2ND 4 (L4)
list. Next, enter the function
Y=
in some location of the
Y=
2ND
in .
L1
(or use ) to
Y3 Y1
.
L2
L2
STAT (LIST) ►
ENTER .
in .
L3
(or use ) to
Y3 Y2
ENTER
2ND
L2
. Press .
ENTER
list, say .
Y1
2
.)
x
to
L4
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