Getting error that NIntegrate has evaluated to non-numerical values

I am trying to evaluate the numerical integration of a very long function and no matter what I do, I get the error that "NIntegrate::inumr: The integrand has evaluated to non-numerical values for all sampling points...". This is the code I have now:

points = 2;
Monitor[Itab =
Table[{{η,
xp, ϕ} = {-3 +
6 (n - 1)/points, .001 + (m - 1) (xpf - 0.001)/
points, -π + (k - 1) 2 π/points};
NIntegrate[Clear[Int]; Int[ϕp_?NumericQ] := (Int[ϕp] =

NIntegrate[ -Z*
x ((3/2 π*RA^3) Sqrt[
RA^2 - x^2 +
b x Cos[ϕp] +b^2/4])(*first part of the field*)((e^2/4 π) Sinh[
Y0] (xp Cos[ϕ] -
x Cos[ϕp]) (τ^2 Sinh[Y0 - η]^2 + xp^2 +
x^2 - 2 xp x Cos[ϕ - ϕp])^(-3/
2) (σ Sinh[
Y0] Sqrt[τ^2 Sinh[Y0 - η]^2 + xp^2 + x^2 -
2 xp x Cos[ϕ - ϕp]]/2 +
1) Exp[σ Sinh[Y0 - η] Sinh[Y0] τ/
2 - σ/2 Sinh[
Y0] Sqrt[τ^2 Sinh[Y0 - η]^2 + xp^2 + x^2 -
2 xp x Cos[ϕ - ϕp]]])(*second part of the \
field*)((e^2/4 π) Sinh[
Y0] (xp Cos[π - ϕ] -
x Cos[ϕp]) (τ^2 Sinh[Y0 + η]^2 + xp^2 +
x^2 - 2 xp x Cos[π - ϕ - ϕp])^(-3/
2) (σ Sinh[
Y0] Sqrt[τ^2 Sinh[Y0 + η]^2 + xp^2 + x^2 -
2 xp x Cos[π - ϕ - ϕp]]/2 +
1) Exp[σ Sinh[Y0 + η] Sinh[Y0] τ/
2 - σ/2 Sinh[
Y0] Sqrt[τ^2 Sinh[Y0 + η]^2 + xp^2 + x^2 -
2 xp x Cos[π - ϕ - ϕp]]]), {x, -Cos[\
ϕp] b/2 + Sqrt[RA^2 - b^2 Sin[ϕp]^2/4],
Cos[ϕp] b/2 + Sqrt[RA^2 - b^2 Sin[ϕp]^2/4]}]);
Int[ϕp], {ϕp, -π/2, π/2}]}, {n, 1,
points + 1}, {m, 1, points + 1}, {k, 1, points + 1}], {n, m, k}];

I would be very thankful if you can tell me what errors you can detect in the code!

I also tried this code:

i1[ϕp_?NumericQ] := i2[ϕp] =
NIntegrate[ -Z*
x ((3/2 π*RA^3) Sqrt[
RA^2 - x^2 +
b x Cos[ϕp] +(*I think there was a sign problem here*)
b^2/4])(*first part of the field*)((e^2/4 π) Sinh[
Y0] (xp Cos[ϕ] -
x Cos[ϕp]) (τ^2 Sinh[Y0 - η]^2 + xp^2 + x^2 -
2 xp x Cos[ϕ - ϕp])^(-3/
2) (σ Sinh[
Y0] Sqrt[τ^2 Sinh[Y0 - η]^2 + xp^2 + x^2 -
2 xp x Cos[ϕ - ϕp]]/2 +
1) Exp[σ Sinh[Y0 - η] Sinh[Y0] τ/
2 - σ/2 Sinh[
Y0] Sqrt[τ^2 Sinh[Y0 - η]^2 + xp^2 + x^2 -
2 xp x Cos[ϕ - ϕp]]])(*second part of the \
field*)((e^2/4 π) Sinh[
Y0] (xp Cos[π - ϕ] -
x Cos[ϕp]) (τ^2 Sinh[Y0 + η]^2 + xp^2 + x^2 -
2 xp x Cos[π - ϕ - ϕp])^(-3/
2) (σ Sinh[
Y0] Sqrt[τ^2 Sinh[Y0 + η]^2 + xp^2 + x^2 -
2 xp x Cos[π - ϕ - ϕp]]/2 +
1) Exp[σ Sinh[Y0 + η] Sinh[Y0] τ/
2 - σ/2 Sinh[
Y0] Sqrt[τ^2 Sinh[Y0 + η]^2 + xp^2 + x^2 -
2 xp x Cos[π - ϕ - ϕp]]]), {x, 0, 5}];
NIntegrate[i2[ϕp], {ϕp, -π/2, π/2}];
• Many of your symbols do not have numeric values. For example, Z, RA, b, e, Y0, $\tau$, $\sigma$, $\phi$, x, xp, maybe others. Examine your integrand first and make sure it evaluates to a numeric value when $\phi p$ is numeric. Note that your integrand does not seem to depend on {n,m,k}. Once the integrand is evaluating to a plausible numeric value, I would then put it into NIntegrate[] and look at a few values. If they look right, I would put the integral into the Table[]. – LouisB Jul 13 '17 at 18:31
• I have numerical values for these: Tc = 170 ; T = 1.5 Tc ; a = 0.15 ; [Zeta] = 1;(* [Kappa]=1.05; )T0 = 10.8; \ fs = 11; b = 7; Y0 = 7.6; Z = 82 ; e = Sqrt[4 [Pi]/137]; Tf = 130 ; t0 = 0.125( fm ); R = 5 ( fm ); RA = 7 ( fm ); [Epsilon] = 1; [Sigma] =(*0.37 (T/Tc)^2) [Zeta] 0.018 T /197; (* fm^-1 *) [Tau] := t0/cosh[[Eta]]; xpf = 5 ; – Susan AB Jul 13 '17 at 18:48
• Do not supply needed numerical values in a comment. Edit your question to so it includes the definitions of these values. – m_goldberg Jul 21 '17 at 3:45
• What happens when you plug in a numerical value for your integration variable into your integrand? (E.g. for NIntegrate[f, {x, 0, 1}] try something like f /. x -> 0.5, substituting your integrand for f, your variable for x, and numerical value in the interval of integration for 0.5.) – Michael E2 Jul 21 '17 at 4:26