Concept explainers
Explanation of Solution
Given information:
The value is
Formula used:
Calculation:
LRAM means left-hand endpoint rectangular approximation method. The name suggests the choice we made when determining the heights of the approximating rectangles: we evaluated the function at the left-hand endpoint of each subinterval.
RRAM means right-hand endpoint rectangular approximation method. The name suggests the choice we made when determining the heights of the approximating rectangles: we evaluated the function at the right-hand endpoint of each subinterval.
In the trapezoidal rule, if [a, b] is partitioned into n subintervals of equal length
That is,
Where,
Therefore,
Conclusion:
Hence it is proved that
Chapter 6 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
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