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I was wondering if a function is absolutely convergent over a certain interval, say,

[tex]

(0,\infty)

[/tex]

will its indefinite integral also be absolutely convergent over the same interval?

Also, assume that f(x) is convergent for

[tex]

(0,\infty).

[/tex]

Would

[tex]

g(x) = \int{\int_{0}^{\infty}f(x)dx}dy &=& {\int_{0}^{\infty}}{\int{f(x)}dydx + {C}

[/tex]

this function, g(x), also be convergent on the same interval as f(x)?

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# Indefinite Integral of an Absolute Convergent Function

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