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Suppose that the graph of [math]f[/math] is concave up at every point of the interval [math][a,b][/math].

• Using the results of Problems Exercise and Exercise, show that
  [[math]] T_{2n} - (T_n - T_{2n}) \lt \int_a^b f \lt T_{2n} , [[/math]]
  for every positive integer [math]n[/math].
• lab{8.3.10b} Hence show that the error [math]|\int_a^b f-T_{2n}|[/math] in the Trapezoid Approximation satisfies
  [[math]] \left| \int_a^b f-T_{2n}\right| \lt |T_n - T_{2n}| . [[/math]]
• Show that \ref{ex8.3.10b} also holds if the graph of [math]f[/math] is concave down at every point of [math][a,b][/math].