7.8 Improper Integrals Review

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