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I have used below code to plot the solution of an integral, but the code doesn't return anything. Could somebody please help me in this regard?

a=0.1;     
Assuming[
      t \[Element] Reals, 
     Plot[Integrate[-Sin[tp] Exp[-((
          16 a  Cos[tp - 2 t + 3 Pi/2] Cos[
            2 tp])/((1 - a^2) \[Pi]))], {tp, 0, 2 Pi}], {t, 0, 2 Pi}]]
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  • $\begingroup$ did you check before plotting if the integrate actually works and it produces solution? it might be that Mathematica could not integrate it. $\endgroup$ – Nasser Dec 6 '19 at 21:16
  • $\begingroup$ It doesn't work! @Nasser $\endgroup$ – Marco Dec 6 '19 at 21:17
  • $\begingroup$ Then this explains why the plot did not work. $\endgroup$ – Nasser Dec 6 '19 at 21:18
  • $\begingroup$ But there might be a way to make it work @Nasser $\endgroup$ – Marco Dec 6 '19 at 21:19
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Integrate does not seem to be able to do it. Try NIntegate

ClearAll[t, tp, a];
a = 0.1;
tick = {Range[0, 2 Pi, Pi/2], Automatic};
foo[t_?NumericQ] := NIntegrate[-Sin[tp] Exp[-((16 a Cos[tp - 2 t + 3 Pi/2] 
      Cos[2 tp])/((1 - a^2) Pi))], {tp, 0, 2 Pi}]

Plot[foo[t], {t, 0, 2 Pi}, Ticks -> tick, GridLines -> tick, 
 GridLinesStyle -> LightGray, PlotStyle -> Red]

Mathematica graphics

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  • $\begingroup$ what is foo[t_?NumericQ]? $\endgroup$ – Marco Dec 6 '19 at 21:26
  • $\begingroup$ @Marco just function name. change it to something else you prefer. $\endgroup$ – Nasser Dec 6 '19 at 21:27
  • $\begingroup$ Is it possible to plot a density plot with variables $a$ and $t$? $\endgroup$ – Marco Dec 6 '19 at 21:36
  • $\begingroup$ @Marco it is probably possible. Please post separate question and and make it clear what is it you are asking for, someone should be able to help. $\endgroup$ – Nasser Dec 6 '19 at 21:38
  • $\begingroup$ why is the argument of the function like this? t_?NumericQ $\endgroup$ – Marco Dec 6 '19 at 21:40

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