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Essential Calculus Early Transcendentals
The left, right, Trapezoidal, and Midpoint Rule approximations were used to estimate $\int_{0}^{2} f(x) d x,$ where $f$ is the function whose graph is shown. The estimates were 0.7811 ,
$0.8675,0.8632,$ and 0.9540 , and the same number of sub-
intervals were used in each case.
(a) Which rule produced which estimate?
(b) Between which two approximations does the true value
of $\int_{0}^{2} f(x) d x$ lie?