Fundamental TheoremThe two halves that make differentiation and integration inverse operations.MathematicsIf f is continuous, then G(x) = the integral of f from ato x is differentiable with G′(x) = f(x).∫ from a to b of f(x) dx = F(b) − F(a)d/dx of ∫ 0 to x of t² dtPart one, directly.∫ from 0 to 1 of 2x dx1F(1) − F(0), F = x².Upper limit is x²f(x²) · 2xChain rule as well.THE COMMON MISTAKEUsing F(b) − F(a) across a discontinuitySplitting the interval at the bad pointThe integral of 1/x² from −1 to 1 is not −2. The integrand blows up at 0, and thetheorem needs an antiderivative on the whole interval.Part two needs f to be integrable and F to be an antiderivative on all of[a, b]. Continuity of f delivers both.Fundamental Theoremlearnposters.com
Fundamental Theorem — printable math wall chart from LearnPosters. Free vector PDF, US Letter and A4.

What’s on the Fundamental Theorem poster

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

Part two needs f to be integrable and F to be an antiderivative on all of [a, b]. Continuity of f delivers both.

Questions about the Fundamental Theorem poster

What’s on the Fundamental Theorem poster?
The rule, 3 worked examples, and the mistake everyone makes. If f is continuous, then G(x) = the integral of f from a to x is differentiable with…; ∫ from a to b of f(x) dx = F(b) − F(a); d/dx of ∫ 0 to x of t² dt = x²; ∫ from 0 to 1 of 2x dx = 1; Upper limit is x² = f(x²) · 2x; Common mistake: Using F(b) − F(a) across a discontinuity → Splitting the interval at…. Part two needs f to be integrable and F to be an antiderivative on all of [a, b]. Continuity of f delivers both.
Who is the Fundamental Theorem poster for?
Fundamental Theorem belongs to the Mathematics section rather than to a school year, because math is not something one grade owns. Anyone learning calculus can pin it up — a beginner, a student mid-course, or someone revising years later.
When should you use the Fundamental Theorem poster?
Every definite integral you evaluate by antiderivative is using part two. A wall chart earns its place by being glanceable from where the work is happening, so Fundamental Theorem belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
What other posters go with Fundamental Theorem?
The Chain Rule, Derivative Rules and Implicit Differentiation sit alongside Fundamental Theorem in the Mathematics section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.The Chain RuleDerivative RulesImplicit Differentiation
Is the Fundamental Theorem poster free to download and print?
Yes. Fundamental Theorem 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 Fundamental Theorem poster print at?
Fundamental Theorem 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 Fundamental Theorem loses nothing.Printing guide

Related posters

Charts that sit alongside Fundamental Theorem on the same wall.

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