Riemann Sums
Kevin Fitzpatrick
CALCULATORS: Casio: fx-9750G Plus & cfx-9850G Series
TI: TI-83 Plus, TI-84 Plus & TI-83/TI-84 Plus Silver Editions
CASIO GRAPHING CALCULATORS
TI GRAPHING CALCULATORS
1. Go to the Main Menu and Choose RUN (#1).
You can do the Riemann Sums on the calculator by
using the Sum and Sequence commands nested
together. To get there, you need to go to:
2nd List right arrow twice 5. This will give you
sum. Then 2nd List right arrow 5. This will give
you seq.
2.
Press OPTN button.
The command accepts five arguments: function,
variable, begin value, end value, increment
Let’s say you want to produce the sequence of
values for f(x)= x2 + 1 for x from 0 to 3 by values of
1 (ie: f(0), f(1), f(2), f(3))
You would do Seq(x2 + 1, x, 0, 3, 1) and you would
get the values shown as a list.
3. Press F4 (CALC) and get :
4. Press F6 for more and get:
If you wanted to add up that list, you could use the
sum command and the ANS command.
5. To enter the summation press F3 and then enter
the following FIVE commands:
If all you wanted was the sum to begin with, do the
two commands together and get the answer at once.
(function, variable, lower limit, upper limit,
increment)
Investigating Linear Equations
1
© Casio, Inc. • For Classroom Use Only
Riemann Sums
continued
CALCULATORS: Casio: fx-9750G Plus & cfx-9850G Series
TI: TI-83 Plus, TI-84 Plus & TI-83/TI-84 Plus Silver Editions
CASIO GRAPHING CALCULATORS
TI GRAPHING CALCULATORS
RIEMANN SUM: Let’s say you want the LOWER
RIEMANN Sum for the same function with 10
subdivisions.
RIEMANN SUM: Let’s say you want the LOWER
RIEMANN Sum for the same function with 10
subdivisions.
1. Calculate the value of the length of the
subdivision using:
right – left
# of divisions
1. Calculate the value of the length of the
subdivision using:
right – left
# of divisions
So here we would have:
3 – 0 = .3 (that’s the base of each rectangle.)
10
So here we would have:
3–0
= .3 (that’s the base of each rectangle.)
10
2. Now to get to the lower sum you start at the
left and stop ONE subdivision short of the right
so that would mean your beginning value is 0,
your end value is 3 –.3 or 2.7 and you are
INCREMENTING by .3 each time.
2. Now to get to the lower sum you start at the
left and stop ONE subdivision short of the right
so that would mean your beginning value is 0,
your end value is 3 –.3 or 2.7 and you are
INCREMENTING by .3 each time.
3. Set up our notation, input it, and solve.
3. Set up our notation, input it, and solve.
4. Thus the Lower Riemann Sum would be:
.3((x2 + 1, x, 0, 2, 7, .3))
4. Thus the Lower Riemann Sum would be:
.3(Sum(Seq(x2 + 1, x, 0, 2, 7, .3))
Now do the Upper Sum. (Note: the answer should
be 13.395.)
No need to go in and out of menus and screens, just
open it up on your home screen and find the value.
THE CASIO ADVANTAGE
•
•
Ease-of-use: Using the fx-9750GPlus, there is
no need to go in and out of menus and screens.
You just open it up on your home screen and
find the value.
The Casio is mor efficient and costs
approximately 1/2 the price of TI.
Investigating Linear Equations
2
© Casio, Inc. • For Classroom Use Only