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gptkbp:instanceOf
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gptkb:integral
gptkb:mathematical_concept
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gptkbp:appearsIn
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real analysis textbooks
undergraduate calculus
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gptkbp:definedIn
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real-valued functions
intervals of real numbers
limit of Riemann sums
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gptkbp:field
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gptkb:mathematics
calculus
real analysis
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gptkbp:generalizes
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gptkb:Henstock–Kurzweil_integral
gptkb:Lebesgue_integral
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gptkbp:introducedIn
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gptkb:19th_century
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gptkbp:limitation
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fails for some highly oscillatory functions
not all bounded functions are Riemann integrable
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gptkbp:namedAfter
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gptkb:Bernhard_Riemann
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gptkbp:notation
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∫_a^b f(x) dx
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gptkbp:property
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linearity
additivity
boundedness required
monotonicity
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gptkbp:relatedTo
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gptkb:Darboux_integral
gptkb:Fundamental_Theorem_of_Calculus
gptkb:Lebesgue_integral
improper integral
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gptkbp:requires
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sum of products of function values and subinterval lengths
partition of interval
sample points
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gptkbp:usedFor
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area under a curve
definite integration
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gptkbp:bfsParent
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gptkb:Lebesgue_integral
gptkb:Bernhard_Riemann
gptkb:Kurzweil_integral
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gptkbp:bfsLayer
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6
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https://www.w3.org/2000/01/rdf-schema#label
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Riemann integral
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