Concept explainers
Let A be the area under the graph of an increasing continuous function f from a to b, 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
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
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