Lesson 5.2
5.2 Improper integrals Quiz: Pearson Edexcel Further Maths, Unit 5
20 questions
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Lesson 5.2, Improper integrals: 20 multiple choice questions for the Pearson Edexcel Further Maths (9FM0), Unit 5: Further calculus, written with Revision Ninja.
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The 20 questions
-
Which feature makes a definite integral an improper integral?
- Fractional exponent
- Discontinuous derivative
- Negative limit
- Infinite limit
-
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 improper integral from 1 to infinity of (1/x) dx?
- Converges to 1
- Converges to ln 2
- Diverges
- Converges to 0
-
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 value of p ensures the improper integral from 1 to infinity of x^(-p) converges?
- p >= 1
- p = 1
- p > 1
- p < 1
-
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
-
What is the behaviour of the improper integral from 0 to infinity of sin x dx?
- Converges to pi
- Converges to 1
- Diverges by oscillation
- Converges to 0
-
If the integral from 1 to infinity of k/x^3 dx equals 4, what is k?
- 16
- 8
- 2
- 4
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