Which of the following describes the behavior of the improper integral $\int_{a}^{b} f(x) \, dx$ if $f(x)$ has an infinite discontinuity at $x=b$?
Question 2
For what values of $p$ does the improper integral $\int_{0}^{1} \frac{1}{x^p} \, dx$ converge?
Question 3
Which of the following statements is true regarding the convergence of $\int_{a}^{\infty} f(x) \, dx$ if $f(x)$ is a positive, continuous, and decreasing function for $x \ge a$?
Question 4
Evaluate the improper integral $\int_{0}^{\infty} \frac{1}{x^2+4} \, dx$.
Question 5
What is the result of applying the Limit Comparison Test to determine the convergence of $\int_{1}^{\infty} \frac{1}{\sqrt{x^4 + 1}} \, dx$?
