Problem 1- approx 1

c0 = {{10, 2.8}, {15, 7.}, {20, 10.8}, {25, 14.1}, {30, 16.5}, {50, 21.4}, {70, 23.3}, {100, 24.5}, {150, 25.3}, {200, 25.8}, {250, 26.2}, {298, 26.6}} ;

<<Statistics`NonlinearFit`

hetC = NonlinearFit[c0, ao + a1 * x/1 + am21/x^2, {x}, {{ao, 32}, {a1, .1}, {am2, 1}}, MaxIterations→1000, Method→Automatic]

BestFitParameters/.NonlinearRegress[c0, ao + a1 * x/1 + am21/x^2, {x}, {{ao, 0}, {a1, 0}, {am2, 0}}, MaxIterations→1000, Method→Automatic, RegressionReport→BestFitParameters]

18.3625 - 1865.9/x^2 + 0.0345806 x

{ao→18.3625, a1→0.0345806, am2→ -1865.9}

Fig1c = ListPlot[c0, PlotRange-> {{0, 300}, {0, 35}}, Frame→True, Prolog→AbsolutePointSize[6]] ;

[Graphics:../HTMLFiles/MATH5_TUT_1_776.gif]

cp[x_] := 18.3625 - 1865.9/x^2 + 0.0345806 x

Fig5c = Plot[{cp[x]}, {x, 0, 300}, Frame→True, PlotRange-> {{0.1, 300}, {0, 35}}, PlotStyle→ {Thickness[0.01]}]

[Graphics:../HTMLFiles/MATH5_TUT_1_779.gif]

-Graphics -

Show[{Fig1c, Fig5c}, Prolog→AbsolutePointSize[6]]

[Graphics:../HTMLFiles/MATH5_TUT_1_782.gif]

-Graphics -

We only integrate from 10 to T

s273 = ∫_10^273cp[x]/xx

60.5005

sf = ∫_10^298cp[x]/xx

62.972

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