The area under y=lnxy=\ln xy=lnx from x=1x=1x=1 to x=2x=2x=2 is bounded using eight rectangles of equal width.
Explain why left-hand endpoints give a lower bound and right-hand endpoints give an upper bound.
Write down expressions for the two bounds as finite sums.
Evaluate both bounds to four decimal places.
Verify that the exact area lies between the bounds.
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.