Lesson 1.08a

1.08a Fundamental theorem of calculus Quiz: OCR Maths, Unit 8

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 1.08a, Fundamental theorem of calculus: 20 multiple choice questions for the OCR Maths (H240), Unit 8: Integration, written with Revision Ninja.

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The 20 questions

  1. What does the definite integral from a to b of f(x) dx equal using an antiderivative F?

    • F(b) + F(a)
    • F'(b) - F'(a)
    • F(b) - F(a)
    • F(a) - F(b)

  2. Which mathematical operation is the inverse of differentiation?

    • Exponentiation
    • Integration
    • Substitution
    • Factorisation

  3. What type of mathematical object is the result of a definite integral?

    • A vector field
    • A function family
    • A single number
    • A differential equation

  4. Evaluate the integral from 1 to 3 of 2x dx.

    • 8
    • 9
    • 6
    • 4

  5. What is d/dx of the integral from 0 to x of t^2 dt?

    • x^3
    • 2x
    • x^2
    • x^3/3

  6. Evaluate the integral from 0 to pi of cos x dx.

    • 0
    • 1
    • 2
    • -1

  7. Evaluate the integral from 1 to e of 1/x dx.

    • 1/e
    • 1
    • 0
    • e

  8. Evaluate the integral from -1 to 2 of f'(x) dx, where f(x) = x^3 - x.

    • 2
    • 6
    • 0
    • 12

  9. What is d/dx of the integral from 2 to x of e^t dt?

    • e^2
    • e^x
    • 0
    • e^x - e^2

  10. What is the integral from a to a of f(x) dx?

    • 0
    • a f(a)
    • f(a)
    • 1

  11. For F(x) = x^3 - 2x, evaluate the integral from 0 to 2 of (3x^2 - 2) dx.

    • 6
    • 4
    • 8
    • 2

  12. If the integral from 0 to k of 2x dx equals 9 with k > 0, what is k?

    • 81
    • 4.5
    • 9
    • 3

  13. Evaluate the integral from 0 to pi/2 of cos x dx.

    • pi/2
    • 1
    • -1
    • 0

  14. What happens to the constant of integration when evaluating a definite integral?

    • It remains arbitrary
    • It doubles
    • It becomes zero
    • It cancels out

  15. In the fundamental theorem of calculus, what relation must F(x) have to f(x)?

    • F'(x) = f(x)
    • F(x) = f'(x)
    • F(x)f(x) = 1
    • F''(x) = f(x)

  16. According to the fundamental theorem of calculus, what does the integral of F'(x) from a to b equal?

    • F(a) - F(b)
    • F(b) + F(a)
    • F(b) - F(a)
    • F'(b) - F'(a)

  17. What is d/dx of the integral from 1 to x of t dt?

    • 1
    • x - 1
    • x^2/2
    • x

  18. Evaluate the integral from 1 to 2 of 4x^3 dx.

    • 17
    • 15
    • 16
    • 8

  19. What is d/dx of the integral from 0 to x of sin t dt?

    • -cos x
    • sin x
    • 1 - cos x
    • cos x

  20. Evaluate the integral from 0 to 1 of f'(x) dx, where f(x) = e^x.

    • e - 1
    • e
    • e + 1
    • 1

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