Various exercises relating to improper integrals.

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

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

Sample Exam Questions

Only one of the following four improper integrals diverges. Choose that improper integral and justify why it diverges. (You need NOT justify why the other integrals converge.)