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Mathematics
Calculus
Why is this definite integral a single number?
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[QUOTE="pasmith, post: 6899785, member: 415692"] This is a consequence of the definition of the Darboux integral. The upper and lower sums of a real-valued function with respect to a partition are real numbers by closure of addition and multiplication. The lower integral, as the supremum of the lower sums, is a real number by the least upper bound axiom; the upper integral, as the infimum of the upper sums, is a real number by the same axiom. A function is integrable if and only if these two numbers are equal, in which case the value of the integral is that number. [/QUOTE]
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Forums
Mathematics
Calculus
Why is this definite integral a single number?
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