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I am having a misunderstanding with Mathematica about integration of InterpolatingFunction. Consider this example:

n = 300
start = 0;
end = 6 π;
testdata = Table[{N[i*end/n], N@Sin[i*end/n]}, {i, 0, n}];
ftest = Interpolation[testdata, InterpolationOrder -> 1]

Now integrate once the interpolating function:

iftest[x_] := Integrate[ftest[t], {t, start, x}];
Plot[{iftest[x], 1 - Cos[x]}, {x, start, end}, 
 PlotStyle -> {Directive[Orange, Thickness[0.01]], Blue}]

Giving as expected. Now, let's integrate once more:

iiftest[x_] := Integrate[iftest[t], {t, start, x}];

then upon trying to plot, i receive complaint: NIntegrate::nlim: t = t is not a valid limit of integration.. So I try:

iiftest[start + 0.2]

only to receive:

enter image description here

Why?

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1 Answer 1

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An easy workaround, because ftest is a pure function(interpolation object), using Derivative

Plot[{Derivative[-1][ftest][t], Derivative[-2][ftest][t]}, {t, start,end}]

enter image description here

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