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Improper integrals are defined in terms of
limits
int (bounds a, infinite)(f(x)dx)
lim (r goes to infinite) int (bounds a, r)(f(x)dx)
if f(x) has a discontinuity at x =a only, then
int (bounds a, b)(f(x)dx)
lim (r goes to a^+) int (bounds r, b)(f(x)dx)
if the limit exists and is finite
the improper integral is convergent
If the limit does not exist or is infinite
the improper integral diverges