First fundamental theorem of calculus
GPTKB entity
Statements (21)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
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| gptkbp:alsoKnownAs |
gptkb:FTC1
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| gptkbp:appliesTo |
continuous functions
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| gptkbp:consequence |
enables computation of definite integrals
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| gptkbp:date |
17th century
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| gptkbp:field |
calculus
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| gptkbp:formedBy |
gptkb:Gottfried_Wilhelm_Leibniz
gptkb:Isaac_Barrow gptkb:Isaac_Newton |
| gptkbp:hasPart |
If f is continuous on [a, b] and F is an antiderivative of f on [a, b], then ∫ₐᵇ f(x) dx = F(b) - F(a).
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| https://www.w3.org/2000/01/rdf-schema#label |
First fundamental theorem of calculus
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| gptkbp:implies |
integration and differentiation are inverse operations
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| gptkbp:partOf |
gptkb:fundamental_theorem_of_calculus
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| gptkbp:relatedTo |
differentiation
integration |
| gptkbp:state |
The integral of a function over an interval can be computed using any one of its infinitely many antiderivatives.
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| gptkbp:usedIn |
engineering
mathematical analysis physics |
| gptkbp:bfsParent |
gptkb:Fundamental_theorem_of_calculus
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| gptkbp:bfsLayer |
6
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