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Chapter 6: Q. 69 (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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Consider the region between the graph of and the x-axis on [1,3]. For each line of rotation given in Exercises 31鈥� 34, use definite integrals to find the volume of the resulting solid.
Use antidifferentiation and/or separation of variables to solve the given differential equations. Your answers will involve unsolved constants.
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?
For each pair of definite integrals in exercise 13-18 decide which if either is larger without computing the integrals
Consider the region between the graph of and the x-axis on [2, 5]. For each line of rotation given in Exercises 35鈥�40, use definite integrals to find the volume of the resulting
solid.
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