how to solve double integral with mathematica?

Questions
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1

Hello everyone, I am trying to solve the double integral written in the file attached. Please help me out. Many thanks in advance.

2

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.

3

thanks a lot.