Lesson 1.08g

1.08g Integration as summation Quiz: OCR Maths, Unit 8

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 1.08g, Integration as summation: 20 multiple choice questions for the OCR Maths (H240), Unit 8: Integration, written with Revision Ninja.

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The 20 questions

  1. Integration as the limit of a sum approximates area using which geometric shapes?

    • Sectors
    • Triangles
    • Rectangles
    • Trapeziums

  2. With n equal strips on [a, b], what is the width of each strip?

    • (b + a)/n
    • (b - a)/n
    • b - a
    • n/(b - a)

  3. In a Riemann sum, what two dimensions are multiplied for each individual strip?

    • Height and gradient
    • Area and perimeter
    • Height and width
    • Gradient and width

  4. For y = x on [0, 4] with four unit-width rectangles using right endpoints, what is the total area of the rectangles?

    • 8
    • 6
    • 4
    • 10

  5. For y = x^2 on [0, 2] with two rectangles of width 1 using left endpoints, what is the total area?

    • 1
    • 5
    • 2
    • 4

  6. For y = x^2 on [0, 2] with two rectangles of width 1 using right endpoints, what is the total area?

    • 5
    • 1
    • 3
    • 4

  7. What is the area under y = x from 0 to 1 as a limit of sums?

    • 1
    • 0
    • 1/2
    • 1/4

  8. For y = x^2 on [0, 2] with four equal strips using right endpoints, what is the sum?

    • 4.5
    • 3.75
    • 2.67
    • 2.5

  9. In integration as the limit of a sum, what value does the number of strips approach?

    • One
    • Infinity
    • Pi
    • Zero

  10. For a decreasing function on [a, b], what is the right-endpoint sum compared with the area?

    • An overestimate
    • Cannot be compared
    • An underestimate
    • Exact

  11. Using two left-endpoint rectangles for y = 1/x on [1, 2], what is the total area?

    • 5/6
    • 7/12
    • 2/3
    • 3/2

  12. For an increasing function on [a, b], what is the left-endpoint sum compared with the area?

    • Zero
    • An underestimate
    • Exact
    • An overestimate

  13. Using two right-endpoint rectangles for y = 1/x on [1, 2], what is the total area?

    • 7/12
    • 2/3
    • 1/2
    • 5/6

  14. For right endpoints with n strips on [0, 1] for y = x, what is the simplified sum?

    • n/(n + 1)
    • (n - 1)/(2n)
    • (n + 1)/n
    • (n + 1)/(2n)

  15. Which definite integral is represented by the limit of the sum of (i/n)^2 (1/n) as n tends to infinity?

    • Integral x^3 from 0 to 1
    • Integral x from 0 to 1
    • Integral x^2 from 0 to infinity
    • Integral x^2 from 0 to 1

  16. What value does the strip width approach in the limit of a sum?

    • Infinity
    • Zero
    • Constant value
    • One

  17. What is the sum of the first n positive integers?

    • n(n - 1)/2
    • (n + 1)/2
    • n^2/2
    • n(n + 1)/2

  18. Using rectangles, what is the integral of x^3 from 0 to 1?

    • 1/2
    • 1/3
    • 1
    • 1/4

  19. Ten rectangles of height 2 and width 0.1 approximate the integral from 0 to 1 of 2 dx. What is the total?

    • 20
    • 0.2
    • 1
    • 2

  20. What does a finite Riemann sum calculate prior to taking the limit?

    • Exact area
    • Approximate area
    • Exact arc length
    • Derivative value

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