Math 2300 Section 005 – Calculus II – Fall 2010
Comparison of Improper Integrals Examples – September 13, 2010
Comparison of Improper Integrals

Solution: This is example 1 from Section 7.8 in the text.

Converge or Diverge?
Solution: Notice that for we have
and so
and so this integral diverges. Notice that starting the integral limit at makes no difference here. The simple fact is that we know
is infinite, while the integral
is finite for any satisfying . It is really the integral on the far left, the one with the infinite limit, that causes the problem here.