Hi,
one of the problems in both notebooks is that you have not declared A in the equation for lct[t]. The numerical integration will not work like that.
Mathematica says that the integral does not converge sufficiently well, and gives three suspected reasons for it:
Numerical integration converging too slowly; suspect one of the
following: singularity, value of the integration is 0, highly
oscillatory integrand, or WorkingPrecision too small.
The integrand appears to be very nasty indeed.
If I change your 3.1416 to Pi
ClearAll["Global`*"]
lmean = 0.8814;
lc = 0.5613;
Af = 1.2;
u = 0.1;
a = 1.0813;
b = 1.2;
p = 1;
q = 2.5294;
lct[t_] := lc*(1 - Af*Tan[t])/(Exp[u*t])
f[l_] := a*b*l^(b - 1)*Exp[-a*l^b]
g[t_] := ((Sin[t])^(2*p - 1)*(Cos[t])^(2*q - 1))/
Chop[(Integrate[(Sin[w])^(2*p - 1)*(Cos[w])^(2*q - 1), {w, 0,
Pi/2}])]
NIntegrate[
f[l]*g[t]*(l/lmean)*(1 -
Af*Tan[t])*(1 - (lc*(1 - Af*Tan[t])/(2*l*Exp[u*t]))), {t, 0,
Pi/2}, {l, 0, lct[t]}]
I get
During evaluation of In[184]:= NIntegrate::zeroregion: Integration
region
{{1.,0.99999999999999415148564447489073961419065634827050978249802712372},{0.25,0.5}}
cannot be further subdivided at the specified working precision.
NIntegrate assumes zero integral there and on any further indivisible
regions. >>
During evaluation of In[184]:= 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. >>
During evaluation of In[184]:= NIntegrate::ncvb: NIntegrate failed to
converge to prescribed accuracy after 18 recursive bisections in t
near {t,l} =
{0.99999999998256007485943732904080818950806429498343042006069936178,0.499962}.
NIntegrate obtained
-6.7530887552778382916336050578428251258689827762888800560827789037310^893804534628964+5.4691121715425751471977471775999760599853203693952910350123540463610^893804534628964
I and
-6.7530887552778382916336050578428251258689827762888800560827789037310^893804534628964+5.4691121715425751471977471775999760599853203693952910350123540463610^893804534628964
I for the integral and error estimates. >>
Out[184]= -6.75308875527783810^893804534628964 +
5.46911217154257510^893804534628964 I
In fact, if you set the Precision to infinity
lmean = SetPrecision[0.8814, Infinity];
lc = SetPrecision[0.5613, Infinity];
Af = 6/5;
u = 1/10;
a = SetPrecision[1.0813, Infinity];
b = SetPrecision[1.2, Infinity];
p = 1;
q = SetPrecision[2.5294, Infinity];
lct[t_] := lc*(1 - Af*Tan[t])/(Exp[u*t])
f[l_] := a*b*l^(b - 1)*Exp[-a*l^b]
g[t_] := ((Sin[t])^(2*p - 1)*(Cos[t])^(2*q -
1))/(Integrate[(Sin[w])^(2*p - 1)*(Cos[w])^(2*q - 1), {w, 0,
Pi/2}])
NIntegrate[f[l]*g[t]*(l/lmean)*(l/(2*lc))*Exp[u*t], {t, 0, Pi/2}, {l, 0, lct[t]}]
You get - at least in MMA10- an error message. If you click on "show all" you get a rather detailed output that shows what is going on.
Cheers,
Marco