plotting - How to integrate numerically the product of result of NDsolve?

I am going to integrate the product of the results of NDsolve, in fact If x and y are the results as interpolating function, How I can integrate x*y numerically?

Table[{Exp[Integrate[ x[t] /. s, {t, 0, i}]]}, {i, -17.5, 10, 1}]

This line does not work for products of x[t]*y[t] or x[t]^2.

This is my entire code file:

yy = {10^-4}; rr = {0.999}; xx = {10^-15}; zz = {10^-4}; mm = {10^-4};


yy + rr + xx^2 + zz - mm^2 - zz^2/24 ic = -17.5

s = NDSolve[{D[y[t], 
     t] == (3 y[t])/5 - (12 m[t]^2 y[t])/5 + (2 r[t] y[t])/
      5 - (6 x[t]^2 y[t])/5 + (3 y[t]^2)/5 + (7 y[t] z[t])/
      5 - (y[t] z[t]^2)/10, 
   D[r[t], t] == -((2 r[t])/5) - (12 m[t]^2 r[t])/5 + (2 r[t]^2)/
      5 - (6 r[t] x[t]^2)/5 + (3 r[t] y[t])/5 + (7 r[t] z[t])/
      5 - (r[t] z[t]^2)/10, 

   D[x[t], t] == (9 x[t])/5 - (6 m[t]^2 x[t])/5 + (r[t] x[t])/
      5 - (3 x[t]^3)/5 + (3 x[t] y[t])/10 + (x[t] z[t])/
      5 - (x[t] z[t]^2)/20, 
   D[z[t], t] == 
    12/5 + (12 m[t]^2)/5 - (12 r[t])/5 - (24 x[t]^2)/5 - (18 y[t])/
      5 - (18 z[t])/5 - (6 m[t]^2 z[t])/5 + (r[t] z[t])/
      5 - (3 x[t]^2 z[t])/5 + (3 y[t] z[t])/10 + (13 z[t]^2)/10 - 
     z[t]^3/20, 
   D[m[t], t] == -2 Sqrt[3] - (6 m[t])/5 - 
     2 Sqrt[3] m[t]^2 - (6 m[t]^3)/5 + 

     2 Sqrt[3] r[t] + (m[t] r[t])/5 + 
     2 Sqrt[3] x[t]^2 - (3 m[t] x[t]^2)/5 + 
     2 Sqrt[3] y[t] + (3 m[t] y[t])/10 + 
     2 Sqrt[3] z[t] + (6 m[t] z[t])/5 - 
     z[t]^2/(4 Sqrt[3]) - (m[t] z[t]^2)/20, x[ic] == xx, y[ic] == yy, 
   m[ic] == mm, z[ic] == zz, r[ic] == rr}, {x, y^2, z, m, r}, {t, ic, 
   10}]

Table[{Exp[Integrate[x[t] /. s, {t, 0, i}]]}, {i, -17.5, 10, 1}]

Comments

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