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Chapter 6: Q. 56 (page 523)
The region between the graph of and the x-axis on [0, 4], revolved around the x-axis.
The volume is
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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.
Sketching a representative disks ,washers and shells : sketch a representative disks , washers , shells for the solid obtained by revolving the regions shown in figure around the given lines .
The x axis
How does a slope field help us to understand the solutions of a differential equation? How can a slope field help us sketch an approximate solution to an initial-value problem?
The area of the surface obtained by revolving the curve
around the x-axis on.
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?
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