Math 182

Feb 15, 2013

Determine whether or not each of the following improper integrals converges.

(diverges) (converges)

Recall the comparison property for definite integrals: If f(x) ≤ g(x) for all x in [a,b] then .

This property is very useful in determining whether some improper integrals converge too:

The comparison test:

If 0 ≤ f(x) ≤ g(x) for all x ≥ a, and if converges, then so does .

If f(x) ≥ g(x) ≥ 0 for all x ≥ a, and if diverges, then so does .

Use a well chosen comparison to determine whether each of the following integrals converges or diverges:

Compare to compare to

Explain why a comparison with will not help you to determine whether converges or not.

(hint: which is larger? Why is that a problem?)

Does converge? Justify your answer!

(hint: it does, but even though the previous comparison doesn’t help, another well chosen one might)