You will be working with the function , and the interval you will always be concerned about is [-2, 6].
The actual area under the curve on the interval [−2, 6] is about 17.586.
Approximating the area under the curve on the interval [−2, 6] by using a Riemann sum with 4 equal subdivisions and left-hand endpoints gives you
R = 2(f(−2) + f(0) + f(2) + f(4)) = 14.976. Draw the rectangles used for this Riemann sum on one of your paper graphs. Do you see where the error for this approximation is?
Approximating the area under the curve on the interval [−2, 6] by using a Riemann sum with 4 equal subdivisions and right-hand endpoints gives you
R = 2(f(0) + f(2) + f(4) + f(6)) = 21.314. Draw the rectangles used for this Riemann sum on one of your paper graphs. Do you see where the error for this approximation is?
The TI-83+ gives the expected 14.976, but the HP-50G gives the complex coordinate (5.357209, 2.35075461244), though it does not list
.