In[1]:= f1 = (1 - Exp[-5.5/Cos[y]])*Sin[y];
In[2]:= xmin = 0;
In[3]:= xmax = Pi;
In[4]:= ymin = 0;
In[5]:= ymax =
ArcTan[300*Cos[x] + Sqrt[12.2500000000 - 90000*(Sin[x])^2]];
In[7]:= NIntegrate[f1, {x, xmin, xmax}, {y, ymin, ymax}]
Out[7]= 3.13316 - 1.0442*10^-9 I
I expect that the imaginary part is due to the fact a numerical method was used.
