Date: Apr 5, 2014 1:49 AM
Author: Hagwood, Charles R.
Subject: question


I am so sick of Mathematica. It no longer seems to be a package to do applied work, but more for the university types. I have spent several hours using several combinations
of ?NumberQ in the following code, but still I get an error. Last weekend I spend several hours using FunctionExpand to get results I can read.

Any help appreciated.



r1=1;
r2=2;
beta2[t_]:={r1*Cos[2*Pi*t],r2*Sin[2*Pi*t]}

beta1[t_]:=beta2[t+4.8*t^2*(t-1)^2]

q2[t_]:=
FunctionExpand[beta2'[t]/Sqrt[Norm[beta2'[t]]],Assumptions->t\[Element] Reals && beta2'\[Element]Vectors[2,Reals]]

q1[s_]:=FunctionExpand[
beta1'[s]/Sqrt[Norm[beta1'[s]]],Assumptions->s\[Element] Reals&& beta2'\[Element]Vectors[2,Reals]]


a[t_, z_] := 2*q1[t].q2'[z] // FunctionExpand
b[t_, z_] := q1[t].q2[z] // FunctionExpand
c[t_, z_] := 2*q1'[t].q2[z] // FunctionExpand


F1[t_, z_] := c[t, z]/b[t, z]
F2[t_, z_] := a[t, z]/b[t, z]



factor1[s_, z_] := Exp[-NIntegrate[F2[s, u], {u, 0, z}]]

factor2[s_, z_] := Exp[NIntegrate[F2[s, u], {u, 0, z}]]

g[s_, z_?NumberQ] := NIntegrate[factor2[s, tau]*F1[s, tau], {tau, 0, z}]

y[s_, z_] := factor1[s, z]*g[s, z]

y[.2, .3]


I get the error

NIntegrate::nlim: _u_ = _tau_ is not a valid limit of integration