Comparing Riemann Sums Consider a trapezoid of area 4 square units bounded by the graphs of y = x, y = 0, x = 1, and x = 3.
(a) Sketch the graph of the region.
(b) Divide the interval [1, 3] into n equal subintervals and show that the endpoints of the subintervals are
(c) Show that the left Riemann sum is
(d) Show that the right Riemann sum is
(e) Use a graphing utility and the program in Example 4 to complete the table.
n | 5 | 10 | 50 | 100 |
Left sum, SL | ||||
Right sum, SR |
(f) Show that
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