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Chapter 6: Q 50 (page 557)
Find the work described in each of Exercises 49–60.
The work required to lift a bathtub full of water 30 feet into the air, given that the bathtub itself weighs 150 pounds and it holds a rectangular volume of water measuring 5 feet by 2 feet by 2 feet.
Work required is 41,940 foot pounds .
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Suppose your bank account grows at percent interest yearly, so that your bank balance after years is .
(a) Show that your bank balance grows at a rate proportional to the amount of the balance.
(b) What is the proportionality constant for the growth rate, and what is the corresponding differential equation for the exponential growth model of ?
Find the exact value of the arc length of each function f (x) on [a, b] by writing the arc length as a definite integral and then solving that integral.
,
Sketching disks ,washers and shells : sketch the three disks , washers , shells that result from revolving the rectangles shown in the figure around the given lines
the x-axis .
For each pair of definite integrals in Exercises 13–18, decide which, if either, is larger, without computing any integrals.
Each of the definite integrals in Exercises 19–24 represents the volume of a solid of revolution obtained by rotating a region around either the x- or y-axis. Find this region.
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