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 rectangles representing Rn - Ln can be reassembled to form a single rectangle whose area is the right side of the equation.
(c) Deduce that

Transcribed Image Text:

b a R, A