Chapter 3-Riemann Sums.
Exploratory Activity #5
Step 1. Notice that your “Upper Bound” is on the coordinate point (8,0) and your “Lower Bound” is on
the coordinate point (2,0).
-- The difference in the x-coordinates between these two points is ________
Step 2. Click the box labeled “Riemann Sums.”
Step 3. Slide the black dot labeled “Partitions(n)” all the way to the left. Do the same for the dot labeled
“Left, Right, Midpoint?”
𝑛
--What is your ∆𝑋 ? _________. What is your ∑𝑖=1 𝑓(𝑥𝑖 ) ∆𝑋 ? ______
Step 4. Take the black dot labeled “Left, Right, Midpoint?” and move it to the right once. What do you
observe about your function and ∆𝑋?
________________________________
Step 5. Do Step 4 again, but this time make sure the black dot is all the way to the right. What do you
observe?
_________________________________
Step 6. Place the black dot back to the Left. Move the black dot labeled “Partitions(n)” all the way to the
right. What is your Riemann sum equal to now? __________
Step 7. Do this for the Midpoint and the Right Riemann sum. What are your Riemann sums for
Midpoint: ____________
Right: ______________
---What do can you conclude from the three Riemann Sums? (i.e. Which is larger, which is smaller)
Step 8. Click the box “Show Riemann Sums” and then Click the box “Show Actual Integral.” You should
now only see the integral for the graph.
--What is the calculated integral? __________
-- In your own words, which Riemann Sum has the closets value to that of the Integral equation?
______________
Also, why do you think that that is the best choice and what connection can you make about Riemann
Sums and Integrals?