You can calculate simple right and
left-hand sums (200 or fewer rectangles) for definite integrals on the
TI-83 as follows:
- Enter the formula for the integrand f(x) in Y1
- Press the blue Y = key.
- Type in the formula, being sure to use the variable X button (just to the right of the green [ALPHA] key).
- Press [2nd] [LIST] [MATH] [5: sum( ] to copy the sum( command to your home-screen.
- Press [2nd] [LIST] [OPS] [5: seq( ] to copy the seq( command to your home-screen.
- Enter
Y1(X),X,start,stop,step))
where Y1 comes from
pressing [VARS] [Y-VARS] [FUNCTION] [1:Y1],
the comma key is just above the [7] key,
X comes from the graphing variable button [X,T,θ,n],
start is the numeric value for the first value of X in the sum (a for a left-sum, a + dx for a right-sum),
stop is the numeric value for the last value of X in the sum (b - dx for a left-sum, and b for a right-sum),
and step is the width of your rectangles. Press [ENTER] to execute the command.
Shown below is a screen shot for calculating a right-hand sum from a = 2 to b = 3 using 10 rectangles (so dx = 0.1).
the comma key is just above the [7] key,
X comes from the graphing variable button [X,T,θ,n],
start is the numeric value for the first value of X in the sum (a for a left-sum, a + dx for a right-sum),
stop is the numeric value for the last value of X in the sum (b - dx for a left-sum, and b for a right-sum),
and step is the width of your rectangles. Press [ENTER] to execute the command.
Shown below is a screen shot for calculating a right-hand sum from a = 2 to b = 3 using 10 rectangles (so dx = 0.1).