Problem 1- approx 2

We are going to inclide more powers of T

c1 = {{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`

hetCb = NonlinearFit[c1, ao + a1 * x/1 + am21/x^2 + a2 x^2 + a3 x^3, {x}, {{ao, 32}, {a1, .1}, {a2, .1}, {a3, .1}, {am2, 1}}, MaxIterations→1000, Method→Automatic]

8.85065 - 978.579/x^2 + 0.306453 x - 0.00170318 x^2 + 2.9546*10^-6 x^3

{ao→8.85065, a1→0.306453, a2→ -0.00170318, a3→2.9546*10^-6, am2→ -978.579}

Fig1c = ListPlot[c1, PlotRange-> {{0, 300}, {0, 35}}, Frame→True, Prolog→AbsolutePointSize[6]] ;

[Graphics:../HTMLFiles/MATH5_TUT_1_795.gif]

cpb[x_] := 8.85065 - 978.579/x^2 + 0.306453 x - 0.00170318 x^2 + 2.9546*10^-6 x^3

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

[Graphics:../HTMLFiles/MATH5_TUT_1_798.gif]

-Graphics -

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

[Graphics:../HTMLFiles/MATH5_TUT_1_801.gif]

-Graphics -

We only integrate from 0 to T

s273 = ∫_10^273cpb[x]/xx

61.6337

sf = ∫_10^298cpb[x]/xx

63.9376

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