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what is the main difference between proper integrals & improper integrals?

Mathematics
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Basically, as far as I gather, improper integrals are those which involve infinities in one of their endpoints (a,b etc.) are +/- infinity (this includes asymptotes (infinite on the y-axis) and when a/b= infinity (infinite on the x-axis)). That's as far as my meagre knowledge stretches, hope it helps.
An integral becomes improper for two reasons: i) Either the upper or lower limit is infinite ii) If a point of discontinuity exists on the interval is being integrated. For example, the following is a improper integral because it's upper bound is infinite: ∫ e^(-x) dx (from x=0 to infinity). This next one is improper due to the discontinuity at x = 0: ∫ 1/√x dx (from x=0 to 1). Of course, there are integrals that are improper for both reasons (having a discontinuity on the integration interval AND having an un-bounded end-point).
so proper inegrals are those without intervals?

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