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1.10.7 Upper and lower bounds using rectangles (A-level only)

1.10.7 Upper and lower bounds using rectangles (A-level only)

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Question 3

The area under y=ln⁡xy=\ln xy=lnx from x=1x=1x=1 to x=2x=2x=2 is bounded using eight rectangles of equal width.

a.

Explain why left-hand endpoints give a lower bound and right-hand endpoints give an upper bound.

[2]
b.

Write down expressions for the two bounds as finite sums.

[2]
c.

Evaluate both bounds to four decimal places.

[2]
d.

Verify that the exact area lies between the bounds.

[2]
Markscheme

1.10.7 Upper and lower bounds using rectangles (A-level only) Questions

  1. A Level
  2. /Maths
  3. /1.10.7 Upper and lower bounds using rectangles (A-level only)

8 exam-style questions on OCR (MEI) A Level Maths 1.10.7 Upper and lower bounds using rectangles (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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