Problem 27E

Let A be the area under the graph of an increasing continuous function f from a to h, and let Ln and Rn be the approximations to A with n subintervals using left and right endpoints, respectively. a How are A, Ln, and Rn related? b Show that RnLn=ban[f(b)f(a)] Then draw a diagram to illustrate this equation by showing that the n rectangles representing Rn – Ln can be reassembled to form a single rectangle whose area is the right side of the equation. c Deduce that RnAban[f(b)f(a)]

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