Left, midpoint and right Riemann sums were used to estimate the area between the graph of f(x) and the x-axis on the interval [3, 7]. We know that f is a function such that f(x)>0 and f'(x)<0 on the interval [3, 7]. The same number of subintervals were used to produce the approximations. The estimates were 1.345, 1.578 and 1.723. Which rule produces each estimate ? Justify your answer.
Left, midpoint and right Riemann sums were used to estimate the area between the graph of f(x) and the x-axis on the interval [3, 7]. We know that f is a function such that f(x)>0 and f'(x)<0 on the interval [3, 7]. The same number of subintervals were used to produce the approximations. The estimates were 1.345, 1.578 and 1.723. Which rule produces each estimate ? Justify your answer.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Left, midpoint and right Riemann sums were used to estimate the area between the graph of f(x) and the x-axis on the interval [3, 7]. We know that f is a function such that f(x)>0 and f'(x)<0 on the interval [3, 7]. The same number of subintervals were used to produce the approximations. The estimates were 1.345, 1.578 and 1.723.
Which rule produces each estimate ? Justify your answer.
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