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Chapter 6: Q. 14 (page 510)
For each pair of definite integrals in exercise 13-18 decide which if either is larger without computing the integrals
The integralis bigger
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Consider the region between and the x-axis on . For each line of rotation given in Exercises 27–30, use four disks or washers based on the given rectangles to approximate the volume of the resulting solid.
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
Consider the region between the graph of and the x-axis on [2,5]. For each line of rotation given in Exercises 35– 40, use definite integrals to find the volume of the resulting solid.
Use the solution of the differential equation for the Newton’s Law of Cooling and Heating model to prove that as t → ∞, 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?
Use antidifferentiation and/or separation of variables to solve the given differential equations. Your answers will involve unsolved constants.
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