Concept explainers
(a)
To calculate:The upper estimate and lower estimate for the amount of oil being consumed by the generator during the week.
(a)
Answer to Problem 33RE
The lower estimate is 4.392 L and the upper estimate is 4.008 L
Explanation of Solution
Given information:
Oil Consumption on Pathfinder Island A diesel generator runs continuously, consuming oil at agradually increasing rate until it must be temporarily shut down to have the filters replaced.
Formula used:
The lower estimate and upper estimate method is used.
Calculation:
For upper estimate during that week take the value of oil consumption rates from Monday to Sunday, then add the rates and multiplies with 24 because length of subinterval is 1 day and 1 day is equal to 24 hour.
For lower estimate during that week take the value of oil consumption rates from Sunday to Saturday, then add the rates and multiplies with 24 because length of subinterval is 1 day and 1 day is equal to 24 hour.
Conclusion:
The lower estimate is 4.392 L and the upper estimate is 4.008 L
(b)
To find: The amount of oil consumed by the generator during that week.
(b)
Answer to Problem 33RE
The value of the integral is
Explanation of Solution
Given information:
Oil Consumption on Pathfinder Island A diesel generator runs continuously, consuming oil at a gradually increasing rate until it must be temporarily shut down to have the filters replaced.
Formula used:
Calculation:
In the trapezoidal rule, if [a, b] is partitioned into n subintervals of equal length
That is,
Where,
Now, apply the trapezoidal rule with
So,
The given table is shown below,
To apply the trapezoidal rule,
To take ‘sun’ as
Now, substitute the values from given table in this equation, equation has a multiplication factor of 24 because rates are given in liters/hour.
Conclusion:
The value of the integral is
Chapter 6 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
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