Concept explainers
Explanation of Solution
Given information:
Formula used:
Calculation:
To approximate
Where [a, b] is partitioned into an even number n of subintervals of equal length
Hence,
In the trapezoidal rule, if [a, b] is partitioned into n subintervals of equal length
That is,
Where,
Hence,
MRAM means midpoint rectangular approximation method. The name suggests the choice we made when determining the heights of the approximating rectangles, we evaluated the function at the midpoint of each subinterval. Subintervals are taken as
Now
Conclusion:
Hence it is proved that
Chapter 6 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
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