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Chapter 6: Q. 5 (page 573)
Write down definite integrals to express the given geometric quantities :
The arc length of the curve formed byon.
Arc length ofon
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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?
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.
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
Use antidifferentiation and/or separation of variables to solve each of the initial-value problems in Exercises 29–52
Find the exact value of the arc length of each function f (x) on [a, b] by writing the arc length as a definite integral and then solving that integral.
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