Improper Integrals Quizzes, Questions & Answers

Top Trending Improper Integrals Quizzes

Improper Integrals – Advanced Techniques, Comparison & Gamma Links

Challenge yourself with advanced improper integrals that combine symmetry (odd/even functions), absolute convergence comparisons, partial fractions, and substitution across infinite intervals. You’ll evaluate tricky...

Questions: 15 | Attempts: 15 | Last updated: Feb 3, 2026

Sample Question 1
Identify the singularity in the integral of tan(x) from 0 to π/2.

X = 0

X = π/4

X = π/2

There is no singularity.

Sample Question 2
Evaluate the integral of 1/√(4 - x) from 0 to 4.

1, 2

4

8

Diverges

Improper Integrals – Convergence, Comparison & Classic Forms

Build confidence deciding convergence vs divergence. This quiz focuses on p-test behavior, integrals with vertical asymptotes, and common convergent models like exponential decay and arctan-type forms. You’ll also see how...

Questions: 15 | Attempts: 12 | Last updated: Feb 3, 2026

Sample Question 1
An improper integral can have:

A finite limit of integration and a continuous integrand.

An infinite limit of integration or a discontinuous integrand.

Only an infinite lower limit.

Only a discontinuous integrand at an endpoint.

Sample Question 2
Evaluate ∫ from 0 to ∞ of e^(-3x) dx.

1/3

3

0

Diverges

Recent Improper Integrals Quizzes

Improper Integrals – Rigorous Definitions, Tests & Applications

Questions: 15 | Attempts: 11 | Last updated: Feb 3, 2026

Sample Question
Which of the following best describes why the integral of f(x) = 1/(x-3) from x = 0 to x = 5 is classified as an improper integral?

The limits of integration are infinite.

The integrand is continuous everywhere on the interval [0, 5].

The integrand has an infinite discontinuity at x = 3, which lies within the interval of integration.

The function crosses the x-axis at x = 3.

Improper Integrals – Infinite Limits & p-Test Practice

Questions: 15 | Attempts: 11 | Last updated: Feb 3, 2026

Sample Question
Which of the following is an example of an improper integral due to an unbounded integrand?

∫ from 0 to ∞ of e⁻ˣ dx

∫ from 1 to 5 of (1/(x-2)) dx, where the integrand is undefined at x=2.

∫ from -∞ to 0 of x² dx

∫₀¹0 of (x+1) dx

Improper Integrals – Basics, Definitions & First Examples

Questions: 15 | Attempts: 13 | Last updated: Feb 3, 2026

Sample Question
What makes an integral an "improper" integral?

The integrand is a trigonometric function.

The integral has one or both limits infinite or the integrand is unbounded in the interval.

The integral requires the use of substitution to solve.

The integral represents the area of a circle.