Riemann IntegrabilityWhen upper and lower sums meet, and when they never do.Mathematicsf is Riemann integrable on [a, b] when some partitionmakes the upper and lower sums arbitrarily close.∀ε > 0 ∃ partition P : U(f, P) − L(f, P) < εf continuous on [a, b]IntegrableUniform continuity.f monotone on [a, b]IntegrableEven with jumps.Indicator of ℚ on [0, 1]Not integrableU = 1 and L = 0.THE COMMON MISTAKEAssuming bounded implies integrableBounded plus continuity almost everywhereLebesgue's criterion: a bounded f is Riemann integrable exactly when its set ofdiscontinuities has measure zero.Riemann handles bounded functions on bounded intervals. Lebesgueextends the theory to limits, which is why analysis moved on.Riemann Integrabilitylearnposters.com
Riemann Integrability — printable math wall chart from LearnPosters. Free vector PDF, US Letter and A4.

What’s on the Riemann Integrability poster

The rule, 3 worked examples, and the mistake everyone makes.

Riemann handles bounded functions on bounded intervals. Lebesgue extends the theory to limits, which is why analysis moved on.

Questions about the Riemann Integrability poster

What’s on the Riemann Integrability poster?
The rule, 3 worked examples, and the mistake everyone makes. f is Riemann integrable on [a, b] when some partition makes the upper and lower sums…; ∀ε > 0 ∃ partition P : U(f, P) − L(f, P) < ε; f continuous on [a, b] = Integrable; f monotone on [a, b] = Integrable; Indicator of ℚ on [0, 1] = Not integrable; Common mistake: Assuming bounded implies integrable → Bounded plus continuity almost…. Riemann handles bounded functions on bounded intervals. Lebesgue extends the theory to limits, which is why analysis moved on.
Who is the Riemann Integrability poster for?
Riemann Integrability belongs to the Mathematics section rather than to a school year, because math is not something one grade owns. Anyone learning analysis can pin it up — a beginner, a student mid-course, or someone revising years later.
When should you use the Riemann Integrability poster?
Before assuming a bounded function has an integral. A wall chart earns its place by being glanceable from where the work is happening, so Riemann Integrability belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
What other posters go with Riemann Integrability?
Absolute vs Conditional, Bolzano-Weierstrass and Cauchy Sequences sit alongside Riemann Integrability in the Mathematics section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.Absolute vs ConditionalBolzano-WeierstrassCauchy Sequences
Is the Riemann Integrability poster free to download and print?
Yes. Riemann Integrability downloads as a free PDF with no account, no email and no watermark, like everything else in the Mathematics section. Print as many copies as you like for a home, a classroom, a library or a tutoring group; reselling the file is the only thing the licence rules out.Read the licence
What size does the Riemann Integrability poster print at?
Riemann Integrability is a vector PDF laid out for US Letter, and prints on A4 with Fit to page — the same file, no separate download. Because every mark on it is drawn rather than photographed, it stays sharp enlarged to A3, A2 or A1 at a copy shop. Colour carries emphasis only, so a greyscale print of Riemann Integrability loses nothing.Printing guide

Related posters

Charts that sit alongside Riemann Integrability on the same wall.

Browse every Mathematics poster, or start from the full catalogue.