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Chapter 4: Q. 65 (page 373)
Suppose a large oil tank develops a hole that causes oil
to leak from the tank at a rate of gallons
per hour. Construct and then solve a definite integral to
determine the amount of oil that has leaked from the tank
after one day.
gallons oil leaked in a day
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Suppose f is a function whose average value on
is and whose average rate of change on
the same interval is . Sketch a possible graph for f .
Illustrate the average value and the average rate of change
on your graph of f.
Write out all the integration formulas and rules that we know at this point.
If and ,then find the values of each definite integral in Exercises . If there is not enough information, explain why.
.
Given a simple proof that
Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.
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