Statements (33)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:integral
gptkb:mathematical_concept |
| gptkbp:appearsIn |
real analysis textbooks
undergraduate calculus |
| gptkbp:definedIn |
real-valued functions
intervals of real numbers limit of Riemann sums |
| gptkbp:field |
gptkb:mathematics
calculus real analysis |
| gptkbp:generalizes |
gptkb:Henstock–Kurzweil_integral
gptkb:Lebesgue_integral |
| https://www.w3.org/2000/01/rdf-schema#label |
Riemann integral
|
| gptkbp:introducedIn |
19th century
|
| gptkbp:limitation |
fails for some highly oscillatory functions
not all bounded functions are Riemann integrable |
| gptkbp:namedAfter |
gptkb:Bernhard_Riemann
|
| gptkbp:notation |
∫_a^b f(x) dx
|
| gptkbp:property |
linearity
additivity boundedness required monotonicity |
| gptkbp:relatedTo |
gptkb:Darboux_integral
gptkb:Fundamental_Theorem_of_Calculus gptkb:Lebesgue_integral improper integral |
| gptkbp:requires |
sum of products of function values and subinterval lengths
partition of interval sample points |
| gptkbp:usedFor |
area under a curve
definite integration |
| gptkbp:bfsParent |
gptkb:Bernhard_Riemann
|
| gptkbp:bfsLayer |
5
|