# Trouble plotting a function constructed using NIntegrate and FindRoot

Here is my code:

f0[y_] := 1/(E^((1 + y)^2/2)*Sqrt[2*Pi])
f1[y_] := 1/(E^((-1 + y)^2/2)*Sqrt[2*Pi])
l[y_] := f1[y]/f0[y]
opts = {Method -> {Automatic, "SymbolicProcessing" -> None}, AccuracyGoal -> 8}
h0[ϵ0_?NumericQ, ϵ1_?NumericQ] :=
-(ϵ1/(1 - ϵ0)) +
NIntegrate[f0[y]*Boole[l[y] < (1 - ϵ0)/(1 - ϵ1)], {y, -∞, ∞},
{Method -> {Automatic, "SymbolicProcessing" -> None},AccuracyGoal -> 8}] -
((1 - ϵ1) *
NIntegrate[f1[y]*Boole[l[y] < (1 - ϵ0)/(1 - ϵ1)], {y, -∞,∞},
{Method -> {Automatic, "SymbolicProcessing" -> None}, AccuracyGoal -> 8}])/(1 - ϵ0)
hh0[ϵ0_] :=
FindRoot[h0[ϵ0, ϵ1] == 0, {ϵ1, 0.5},
StepMonitor :>Print["Step to ϵ0 = ", ϵ0, Evaluate@opts]]
Plot[hh0[ϵ0], {ϵ0, 0, 1}]


I am able to get all the values that are necessery to plot, but the plot doesnt output any graphics. How can I fix this problem?Improved formatting

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If you try hh0[x] for some values of x, you will see there is a convergence problem with your integrals. –  Jean-Claude Arbaut May 18 at 20:52
@Jean-ClaudeArbaut hh0[0.1] gives me for example 0.77327. hh0[0.5] gives me 0.315573 ... I can get single numbers. Integrals are definitely correct if I havent mistype anything but i tried again. –  Seyhmus Güngören May 18 at 20:55
Interesting, I get the same values, but with lots of messages of this kind: NIntegrate::slwcon: Numerical integration converging too slowly; suspect one of the following: singularity, value of the integration is 0, highly oscillatory integrand, or WorkingPrecision too small –  Jean-Claude Arbaut May 18 at 20:57
@Jean-ClaudeArbaut it is not only you who gets that message. I get many of them. But eventually there is a result)) –  Seyhmus Güngören May 18 at 20:58
Ok, solved. Type Plot[ϵ1 /. hh0[ϵ0], {ϵ0, 0, 1}]. Since you are calling FindRoot, you don't get a value but a list. With /. you can retrieve the value. –  Jean-Claude Arbaut May 18 at 21:02

Since you are calling FindRoot, you don't get a value but a list. With /. you can retrieve the value:
Plot[ϵ1 /. hh0[ϵ0], {ϵ0, 0, 1}]