Lesson 5.2
5.2 Improper integrals Quiz: Pearson Edexcel Further Maths, Unit 5
20 questions
In partnership with Revision Ninja
Lesson 5.2, Improper integrals: 20 multiple choice questions for the Pearson Edexcel Further Maths (9FM0), Unit 5: Further calculus, written with Revision Ninja.
Host it live on the board and students join with a game code on their own devices, or revise alone with Free Play. The answers are revealed in the game.
The 20 questions
-
What makes an integral improper?
- An integrand that is continuous on a finite closed interval
- A result that is negative
- An integrand that is a polynomial of degree at least two
- An infinite limit of integration, or an integrand that is unbounded within the range
-
For which values of p does the integral from 1 to infinity of 1/x^p dx converge?
- p > 1
- p = 1 only
- p < 1
- p >= 0
-
What is the behaviour of the integral from 1 to infinity of 1/x dx?
- It converges to 1
- It converges to 0
- It diverges
- It converges to ln 2
-
What is the value of the integral from 0 to infinity of e^(-x) dx?
- 1
- e
- 0
- infinity
-
What is the value of the integral from 1 to infinity of 1/x^2 dx?
- 1/2
- 2
- infinity
- 1
-
What is the value of the integral from 0 to 1 of 1/sqrt(x) dx?
- 1
- infinity
- 2
- 1/2
-
What is the value of the integral from 0 to 1 of ln x dx?
- 1
- -1
- -2
- 0
-
What is the value of the integral from 0 to infinity of 1/(1 + x^2) dx?
- 1
- pi
- pi/2
- pi/4
-
What is the behaviour of the integral from 0 to 1 of 1/x^2 dx?
- It converges to 2
- It diverges
- It converges to 1
- It converges to -1
-
What is the value of the integral from 2 to infinity of 1/x^3 dx?
- 1/2
- 1/16
- 1/8
- 1/4
-
What is the value of the integral from 0 to infinity of x e^(-x) dx?
- -1
- 1
- 0
- 2
-
What is the value of the integral from 0 to infinity of e^(-2x) dx?
- 1/2
- 2
- -1/2
- 1
-
What is the value of the integral from 0 to 1 of x^(-1/3) dx?
- 3/2
- 2/3
- 1/3
- infinity
-
What is the value of the integral from 0 to 4 of 1/sqrt(4 - x) dx?
- infinity
- 4
- 8
- 2
-
Which of the following integrals converges?
- The integral from 0 to infinity of 1 dx
- The integral from 1 to infinity of 1/x dx
- The integral from 1 to infinity of x^(-3/2) dx
- The integral from 1 to infinity of x^(-1/2) dx
-
What is the value of the integral from 0 to infinity of x^2 e^(-x) dx?
- 6
- 1
- 4
- 2
-
What is the value of the integral from 0 to infinity of x/(1 + x^2)^2 dx?
- 1/4
- 1/2
- 1
- It diverges
-
What is the value of the integral from 0 to 1 of (ln x)^2 dx?
- -2
- -1
- 2
- 1
-
Is the integral from 0 to infinity of sin x dx convergent?
- Yes, it converges to 2
- Yes, it converges to 0 by symmetry
- No, its partial integrals oscillate and have no limit
- Yes, it converges to 1
-
If the integral from 1 to infinity of k/x^3 dx equals 4, what is k?
- 16
- 8
- 2
- 4
Related quizzes
- Proof by mathematical induction Quiz · 1.1 · 20 questions
- Quadratic equations and complex arithmetic Quiz · 2.1-2.2 · 20 questions
- Matrix arithmetic and inverses Quiz · 3.1-3.2 · 20 questions
- Expectation of discrete random variables Quiz · 3B.1.1 · 20 questions
- The Poisson distribution Quiz · 3B.2.1 · 20 questions
- Geometric and negative binomial models Quiz · 3B.3.1 · 20 questions
- Hypothesis tests for the Poisson distribution Quiz · 3B.4.1 · 20 questions
- Applying the Central Limit Theorem Quiz · 3B.5.1 · 20 questions
- Goodness of fit tests for discrete distributions Quiz · 3B.6.1 · 20 questions
- Definition and derivation of probability generating functions Quiz · 3B.7.1 · 20 questions