Plotting solution of an integral

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}]]

• did you check before plotting if the integrate actually works and it produces solution? it might be that Mathematica could not integrate it. Dec 6, 2019 at 21:16
• It doesn't work! @Nasser Dec 6, 2019 at 21:17
• Then this explains why the plot did not work. Dec 6, 2019 at 21:18
• But there might be a way to make it work @Nasser Dec 6, 2019 at 21:19

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]


• what is foo[t_?NumericQ]? Dec 6, 2019 at 21:26
• @Marco just function name. change it to something else you prefer. Dec 6, 2019 at 21:27
• Is it possible to plot a density plot with variables $a$ and $t$? Dec 6, 2019 at 21:36
• @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. Dec 6, 2019 at 21:38
• why is the argument of the function like this? t_?NumericQ Dec 6, 2019 at 21:40