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.
137 exam-style questions on OCR (MEI) A Level Maths 1.10 Numerical Methods (A-level only), covering 1.10.1 Locate roots by change of sign (A-level only), 1.10.2 When change of sign methods fail (A-level only), 1.10.3 Fixed point iteration (A-level only), 1.10.4 Newton-Raphson method (A-level only), 1.10.5 Convergence of iterations (A-level only), 1.10.6 Trapezium rule (A-level only), 1.10.7 Upper and lower bounds using rectangles (A-level only), and 1.10.8 Numerical methods to solve problems (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.