Various exercises relating to improper integrals.

Evaluate the integral: This integral is not improperimproper
because of the behavior of the integrand near .

Use the Direct Comparison Test or the Limit Comparison Test to determine
whether the integral converges or diverges: Answer: the integral convergesdiverges
by directlimit
comparison with the function

Use the Direct Comparison Test or the Limit Comparison Test to determine
whether the integral converges or diverges: Answer: the integral convergesdiverges
by directlimit
comparison with the function (select the largest exponent for the denominator
which makes the statement true).

Use the Direct Comparison Test or the Limit Comparison Test to determine
whether the integral converges or diverges: Answer: the integral convergesdiverges
by direct comparison with the function

Use the Direct Comparison Test or the Limit Comparison Test to determine
whether the integral converges or diverges: Answer: the integral convergesdiverges
by direct comparison with the function

Use the Direct Comparison Test or the Limit Comparison Test to determine
whether the integral converges or diverges: Answer: the integral convergesdiverges
by directlimit
comparison with the function

Use the Direct or Limit Comparison Test to determine whether the integral
converges or diverges: Answer: The integral convergesdiverges
by directlimit
comparison with the function

Use the Direct or Limit Comparison Test to determine whether the integral
converges or diverges: Answer: The integral convergesdiverges
by direct comparison with the function

### Sample Quiz Questions

Which of the following improper integrals is convergent? Show how you used comparison tests to justify your answer.

only converges only converges
only converges and converge and converge and converge

Integral is divergent by direct comparison to the function . Integral is divergent by
limit comparison to the function . Integral is convergent by direct comparison to the
function .

Which of the following improper integrals is convergent? Show how you used comparison tests to justify your answer.

only converges only converges
only converges and converge and converge and converge

Integral is divergent by direct comparison to the function . Integral is convergent by
direct comparison to the function . Integral is convergent by limit comparison to the
function .