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Chapter 6: Q. 68 (page 540)
Set up and solve a definite integral to find the exact area of each surface of revolution obtained by revolving the curve around the x-axis on the interval [a, b].
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Use antidifferentiation and/or separation of variables to solve each of the initial-value problems in Exercises 29鈥�52.
34.
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 line
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 .
Write the volume of the two solids of revolution that follow in terms of definite integrals that represent accumulations of disks and/or washers. Do not compute the integrals.
Suppose an object is heating up according to a model for Newton鈥檚 Law of Cooling with temperature satisfying for some constant .
(a) What is the ambient temperature of the environment under this model?
(b) Given that the temperature T(t) is increasing and that , is the constant positive or negative, and why?
(c) Use the differential equation to argue that the object鈥檚 temperature changes are faster when it is much cooler than the ambient temperature than when it is close to the ambient temperature.
(d) Part (c) is the basis for the oft-misunderstood saying 鈥淐oldwater boils faster.鈥� Why?
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