FTC
E898474
The Fundamental Theorem of Calculus is a central result in calculus that links differentiation and integration by showing they are inverse processes under suitable conditions.
All labels observed (1)
| Label | Occurrences |
|---|---|
| FTC canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10991387 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: FTC Context triple: [Fundamental Theorem of Calculus, alsoKnownAs, FTC]
-
A.
FTC
FTC is a global middle and high school robotics competition program that challenges teams to design, build, and program robots to complete themed tasks.
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B.
Federal Trade Commission
The Federal Trade Commission is an independent U.S. government agency responsible for enforcing antitrust and consumer protection laws to promote fair competition and safeguard consumers.
-
C.
FCC
FCC is the common abbreviation for FC Cincinnati, a professional soccer club based in Cincinnati, Ohio, that competes in Major League Soccer.
-
D.
JFTC
JFTC is a NATO training facility in Bydgoszcz, Poland, focused on preparing joint and combined forces for multinational operations and exercises.
-
E.
FTTA
FTTA is a U.S. law that promotes collaboration and technology transfer between federal laboratories and the private sector to commercialize government-funded innovations.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: FTC Target entity description: The Fundamental Theorem of Calculus is a central result in calculus that links differentiation and integration by showing they are inverse processes under suitable conditions.
-
A.
FTC
FTC is a global middle and high school robotics competition program that challenges teams to design, build, and program robots to complete themed tasks.
-
B.
Federal Trade Commission
The Federal Trade Commission is an independent U.S. government agency responsible for enforcing antitrust and consumer protection laws to promote fair competition and safeguard consumers.
-
C.
FCC
FCC is the common abbreviation for FC Cincinnati, a professional soccer club based in Cincinnati, Ohio, that competes in Major League Soccer.
-
D.
JFTC
JFTC is a NATO training facility in Bydgoszcz, Poland, focused on preparing joint and combined forces for multinational operations and exercises.
-
E.
FTTA
FTTA is a U.S. law that promotes collaboration and technology transfer between federal laboratories and the private sector to commercialize government-funded innovations.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical theorem
ⓘ
mathematical theorem ⓘ mathematical theorem ⓘ theorem in calculus ⓘ |
| alsoKnownAs |
First Fundamental Theorem of Calculus
NERFINISHED
ⓘ
Second Fundamental Theorem of Calculus NERFINISHED ⓘ |
| appliesTo |
functions continuous on a closed interval
ⓘ
real-valued functions ⓘ |
| category | theorems named fundamental ⓘ |
| describes |
evaluation of a definite integral using an antiderivative
ⓘ
relationship between the integral of a function and its antiderivative ⓘ |
| field |
calculus
ⓘ
mathematical analysis ⓘ |
| formalizes | inverse relationship between differentiation and integration ⓘ |
| hasAbbreviation | FTC NERFINISHED ⓘ |
| hasFormula |
If F is an antiderivative of f on [a,b], then ∫_a^b f(x) dx = F(b) − F(a)
ⓘ
If f is continuous on [a,b] and F(x)=∫_a^x f(t) dt, then F′(x)=f(x) ⓘ |
| hasGeneralization |
Lebesgue integral versions
ⓘ
Stieltjes integral versions ⓘ divergence theorem NERFINISHED ⓘ vector calculus theorems such as Green’s theorem ⓘ vector calculus theorems such as Stokes’ theorem ⓘ |
| hasPart |
Fundamental Theorem of Calculus, Part 1
NERFINISHED
ⓘ
Fundamental Theorem of Calculus, Part 2 NERFINISHED ⓘ |
| historicallyAssociatedWith |
Gottfried Wilhelm Leibniz
NERFINISHED
ⓘ
Isaac Newton NERFINISHED ⓘ |
| implies |
definite integrals can be computed using antiderivatives
ⓘ
every continuous function on a closed interval has an antiderivative defined by an integral ⓘ |
| involvesConcept |
antiderivative
ⓘ
antiderivative ⓘ definite integral ⓘ definite integral ⓘ |
| isCentralResultIn |
calculus
ⓘ
mathematical analysis ⓘ |
| relatesConcept |
differentiation
ⓘ
integration ⓘ |
| requiresCondition | integrand is continuous on the interval ⓘ |
| statesRelationship | differentiation and integration are inverse processes under suitable conditions ⓘ |
| timePeriod | 17th century ⓘ |
| topicOf |
advanced analysis textbooks
ⓘ
introductory calculus courses ⓘ |
| underlies |
techniques for computing accumulated quantities
ⓘ
techniques for computing areas under curves ⓘ |
| usedIn |
applied mathematics
ⓘ
multivariable calculus generalizations ⓘ real analysis ⓘ single-variable calculus ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: FTC Description of subject: The Fundamental Theorem of Calculus is a central result in calculus that links differentiation and integration by showing they are inverse processes under suitable conditions.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.