Quantity not represented by the definite integral.
Answer to Problem 46E
The quantity of distance traveled by a train moving at 70 mph for 8 minutes cannot be represented by the definite integral.
Explanation of Solution
Given information:
While integrating
The units of a and b must be same as the units for x .
This implies
While integrating
The units of 0 and 8 must be same as the units for t .
For the quantity of distance traveled by a train moving at 70 mph for 8 minutes:
Since 70 represents miles per hour, but 0 and 8 have units of minutes.
For the quantity of volume of ice cream produced by a machine making 70 gallons per hour for 8 hours:
Thus,
t also has units of hours.
The Problem requires the volume produced in 8 hours.
Then
The bounds of 0 and 8 also have units of hours.
For the quantity of length of track left by a snail traveling at 70 cm per hour for 8 hours:
Thus,
t also has units of hours.
The Problem requires the length of a track for 8 hours.
Then
The bounds of 0 and 8 also have units of hours.
For the quantity of total sales of a company selling $70 of merchandise per hour for 8 hours:
Thus,
t also has units of hours.
The Problem requires the total sales for 8 hours.
Then
The bounds of 0 and 8 also have units of hours.
For the quantity of the amount the tide has risen 8 minutes after low tide if it rises at a rate of 70 mm per minute:
Thus,
t also has units of minutes.
The Problem requires the amount of tide has risen in 8 minutes.
Then
The bounds of 0 and 8 also have units of minutes.
Conclusion:
We can conclude that in option (A), 70 represents miles per hour, but 0 and 8 have units of minutes.
Thus,
The quantity of distance traveled by a train moving at 70mph for 8 minutes cannot be represented by
Therefore,
The correct answer is option (A).
Chapter 6 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
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