Lesson 1.08e

1.08e Areas under and between curves Quiz: OCR Maths, Unit 8

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 1.08e, Areas under and between curves: 20 multiple choice questions for the OCR Maths (H240), Unit 8: Integration, written with Revision Ninja.

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The 20 questions

  1. How is the physical area found for a region lying entirely below the x-axis?

    • Reciprocal of integral
    • Unmodified integral
    • Integral squared
    • Modulus of integral

  2. Which expression gives the area between upper curve f(x) and lower curve g(x) on [a, b]?

    • Integral of (f x g)
    • Integral of (f + g)
    • Integral of (g - f)
    • Integral of (f - g)

  3. Find the area under y = x^2 from x = 0 to x = 2.

    • 4
    • 8/3
    • 2
    • 16/3

  4. Find the area between y = 4 - x^2 and the x-axis from x = -2 to x = 2.

    • 64/3
    • 16/3
    • 32/3
    • 8

  5. Find the area between y = x and y = x^2 for 0 <= x <= 1.

    • 1/3
    • 1/6
    • 1/2
    • 1/12

  6. Find the area between y = 2x + 3 and y = x^2.

    • 9
    • 32/3
    • 16/3
    • 10

  7. Find the area under y = sin x from x = 0 to x = pi.

    • 0
    • pi
    • 1
    • 2

  8. Find the area between y = x(x - 2) and the x-axis for 0 <= x <= 2.

    • 8/3
    • 2/3
    • 4/3
    • -4/3

  9. Find the area between y = e^x, the x-axis, x = 0 and x = 1.

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

  10. Find the area between y = 1/x, the x-axis, x = 1 and x = e.

    • 1/e
    • 1
    • e - 1
    • e

  11. Find the area between y = x^3 - x and the x-axis for -1 <= x <= 1.

    • 0
    • 1
    • 1/2
    • 1/4

  12. Find the area between y = x and y = x^3 for 0 <= x <= 1.

    • 1/4
    • 1/3
    • 1/6
    • 1/2

  13. A curve is given by x = t^2 and y = t for 0 <= t <= 1. What is the area under it?

    • 2/3
    • 1
    • 1/3
    • 1/2

  14. If the area under y = kx from x = 0 to x = 2 is 6, what is k?

    • 6
    • 3
    • 2
    • 12

  15. Find the area under y = x^2 - 4 from x = 0 to x = 2 (as a positive value).

    • -16/3
    • 16/3
    • 4
    • 8/3

  16. Find the area between y = sqrt(x) and y = x^2 for 0 <= x <= 1.

    • 1/3
    • 1/6
    • 2/3
    • 1/2

  17. Why does integrating a curve below the x-axis result in a negative value?

    • x-values are negative
    • y-values are negative
    • Limits are negative
    • Gradients are negative

  18. Find the area between y = 2 and y = x^2.

    • 4 sqrt(2)
    • 4 sqrt(2)/3
    • 2 sqrt(2)
    • 8 sqrt(2)/3

  19. Find the area under y = cos x from x = 0 to x = pi/2.

    • 2
    • 1
    • 0
    • pi/2

  20. Find the area under y = 3 from x = 1 to x = 4.

    • 3
    • 12
    • 9
    • 6

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