The area A A\,A under y=x3+xy=x^3+xy=x3+x from x=1x=1x=1 to x=2x=2x=2 is estimated using 50 equal-width rectangles.
The lower sum is L50=5.1703L_{50}=5.1703L50=5.1703.
Show that the right-endpoint sum is an upper bound.
Without evaluating all 50 right-endpoint heights, find U50U_{50}U50.
Hence give bounds for AAA.
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.