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
Rn-Ln = ((b-a)/n) [f(b) - f(a)]

Question

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
Rn-Ln = ((b-a)/n) [f(b) - f(a)]

anonymous · Answer

Here's a sketch of $A=\displaystyle\int_a^bf(x)\,dx$:
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