Nothing about a Riemann sum needs a formula: a column of readings taken at regular intervals is enough. This is how the rules are actually used, because real measurements arrive as tables.
Speeds at t=0,2,4 are 5,9,7 m/s. Estimate the distance with a left sum.
Each strip is 2 seconds wide.
A left sum uses the readings at the start of each strip, so 5 and 9.
That gives 2 times 5 plus 2 times 9, which is 28 metres.
The answer is 28 m.
Where students go wrong
Adding the readings and multiplying by the width once. Every strip gets its own width, so the width multiplies the whole sum, not one reading, and the trapezoidal rule halves only the two on the ends.
Also called Riemann sum table, estimate from a table, trapezoidal rule from a table or distance from a velocity table.
What you can put on this worksheet
Left Riemann sum
extAcar′sspeedvextinm/sisrecordedatthesetimes.Estimate how far it travels, using a left Riemann sum.tv01621141161289→ 100 m
Right Riemann sum
extAcar′sspeedvextinm/sisrecordedatthesetimes.Estimate how far it travels, using a right Riemann sum.tv01621141161289→ 86 m
The trapezoidal rule
extAcar′sspeedvextinm/sisrecordedatthesetimes.Estimate how far it travels, using the trapezoidal rule.tv01621141161289→ 93 m
Questions about these worksheets
Yes. Every riemann sums from a table sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Calculus is usually taken around 12th grade or a first college course, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the riemann sums from a table questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are two levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
You pick from 3: left riemann sum, right riemann sum and the trapezoidal rule. Tick as many as you want and set how many of each, or let it spread them evenly.
Adding the readings and multiplying by the width once. Every strip gets its own width, so the width multiplies the whole sum, not one reading, and the trapezoidal rule halves only the two on the ends.