From the graph below, determine if each integral converges, diverges, or if its behavior cannot be determined.
(a) We can't tell if
converges or diverges. We know that , but since
diverges, that knowledge doesn't do us any good.
(b) Since and
converges, the integral
must also converge.
(c) We know that
and we know that
converges. However, since we don't know if
converges or diverges, we don't know what
(d) Since and
(e) We can't tell if
converges or diverges. Knowing doesn't help, because
(f) We know that
Since we know that
diverges, the integral
must also diverge.