Concept explainers
(a)
To calculate:The upper estimate and lower estimate for the distance travelled by the shed.
(a)
Answer to Problem 34RE
The lower estimate is 87.15 ft and the upper estimate is 103.05 ft
Explanation of Solution
Given information:
A speedometer in the sled monitors its speed, which is recorded at 3-second intervals during the 27-second run.
Formula used:
The upper estimate and lower estimate method is used.
Calculation:
(a) For upper estimate, sum the speeds from zero second to 24 second and then multiplied by 3, the speeds from 0 second for calculating the upper estimate because values of speed are decreasing. Hence, it is decreasing function and to get an upper estimate in decreasing function, to apply left-hand pint rectangular approximation method.
For lower estimate, sum the speeds from three second to 27 second and then multiplied by 3, the speeds from 3 second for calculating the lower estimate because values of speed are decreasing. Hence, it is decreasing function and to get a lower estimate in decreasing function, to apply right-hand pint rectangular approximation method.
Conclusion:
The lower estimate is 87.15 ft and the upper estimate is 103.05 ft
(b)
To find:the distance travelled by the sled.
(b)
Answer to Problem 34RE
The value of the integral is
Explanation of Solution
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 ‘time’ as
Similarly by taking the remaining tabular values as shown in the following table,
Now, substitute the values from given table in this equation
Conclusion:
The value of the integral is
Chapter 6 Solutions
Calculus: Graphical, Numerical, Algebraic
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University Calculus: Early Transcendentals (4th Edition)
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