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Chapter 6: Q. 50 (page 512)
Consider the region between the graphs of and on [0, 2]. For each line of rotation given in Exercises 47鈥�50, use definite integrals to find the volume of the resulting solid.
The volume of the solid is
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Use antidifferentiation and/or separation of variables to solve the given differential equations. Your answers will involve unsolved constants.
Use the solution of the differential equation for the Newton鈥檚 Law of Cooling and Heating model to prove that as t 鈫� 鈭�, the temperature T(t) of an object approaches the ambient temperature A of its environment. The proof requires that we assume that k is positive. Why does this make sense regardless of whether the model represents heating or cooling?
The volume of solid obtained by revolving the region between the graph around (a)the y axis (b)the line x=2
Use antidifferentiation and/or separation of variables to solve each of the initial-value problems in Exercises 29鈥�52.
29.
For each pair of definite integrals in exercise 13-18 decide which if either is larger without computing the integrals
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