6. Integration and Accumulation of Change

Evaluating Improper Integrals — Quiz

Test your understanding of evaluating improper integrals with 5 practice questions.

Practice Questions

Question 1

What is the main idea of an improper integral with an infinite interval such as $\int_1^\infty f(x)\,dx$?

Question 2

Which integral is improper because the integrand has a vertical asymptote at $x=2$?

Question 3

Which limit represents $\int_0^1 \frac{1}{\sqrt{x}}\,dx$ as an improper integral?

Question 4

Evaluate $\int_1^\infty \frac{1}{x^2}\,dx$.

Question 5

Does $\int_1^\infty \frac{1}{x}\,dx$ converge or diverge?