Viewing topic: Improper Riemann Integrable

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Improper Riemann Integrable

  • Definition: If f is Riemann-integrable on [a,b] for every b >= a, and if the limit as b goes to infinity of int_(from a to b)[f(x)dx] exists, then f is said to be improper Riemann-integrable on [a, infinity) and the improper Riemann integral of f, denoted by int_(from a to infinity)[f(x)dx] is defined by the equation int_(from a to infinity)[f(x)dx] = limit as b goes to infinity of int_(from a to b)[f(x)dx].

    Source: Mathematical Analysis, second edition by Tom M. Apostol

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