Improper Integrals Quizzes, Questions & Answers

All Grades

Top Trending Improper Integrals Quizzes

Improper Integrals – Basics, Definitions & First Examples

Learn what makes an integral “improper” and how to evaluate it using limits. You’ll practice integrals with infinite bounds and integrals where the function becomes unbounded at an endpoint or inside the...

Questions: 15 | Attempts: 12 | Last updated: Dec 16, 2025

Sample Question 1
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.

Sample Question 2
Evaluate the improper integral from 1 to ∞ of (1/x²) dx.

12, 12

1

∞ (diverges)

-1

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: 12 | Last updated: Dec 16, 2025

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

Recent Improper Integrals Quizzes

Improper Integrals â€“ Rigorous Definitions, Tests & Applications

Take your improper integrals to the next level with stronger reasoning tools. You’ll handle internal discontinuities and endpoint singularities using correct splitting and limit notation, and you’ll test convergence...

Questions: 15 | Attempts: 10 | Last updated: Dec 16, 2025

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 â€“ 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: 10 | Last updated: Dec 16, 2025

Sample Question
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.

Improper Integrals â€“ Infinite Limits & p-Test Practice

Strengthen your skills with improper integrals by identifying why an integral is improper and choosing the correct limit setup. You’ll evaluate classic forms involving arctan and exponentials, apply the p-test, and handle...

Questions: 15 | Attempts: 10 | Last updated: Dec 16, 2025

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