void MCintegral()
{
   // In a Compton scattering experiment, a cylindrical aluminium target is put in front 
   // of a punctual source of gamma rays, and the detector is put on the other side.
   // In order to normalize the results, one needs the effective volume, defined by 
   // the intersection between the cylinder and the cone defined by the source and the detector.
   //
   // Compute that volume by MC means, in the following two configurations:
   // a) the cylinder is 10cm high, r=2cm. It is standing vertically at equal distance of the 
   //    source and of the detector, such that the gamma rays enters on the curved side.
   //    The detector window is a circle of r=2cm put at 4m away from the source.
   // b) The distance between source and detector is reduced to 10cm and the cylinder 
   //    is replaced by a smaller one, of radius equal to 1cm.

   Float_t x,y,z;
   int count = 0;
   int N=100000;
   TH3F* h = new TH3F("volume","volume",40,-2,2,40,-2,2,40,-2,2);
   for(int i=0;i<N;++i) {
     // generate random numbers in a cube containing the target volume
     x = gRandom->Uniform(-2,2);
     y = gRandom->Uniform(-2,2);
     z = gRandom->Uniform(-2,2);
     // count the fraction in the target volume
     //if((x*x+y*y)<4 && sqrt(x*x+z*z)<(1-y/200.) ) h->Fill(x,y,z);
     if((x*x+y*y)<1 && sqrt(x*x+z*z)<(1-y/10.) ) h->Fill(x,y,z);
   }
  
   // extract the result
   h->Draw();
   std::cout << "volume is " << h->GetEntries()/N*64. << " cm^3. " << std::endl;

   // in case a, the result (12.2464cm^3) differs by ~2% from the approximation of a cylinder (4pi)
   // case b, would be more difficult to approximate.


   // an alternative (more efficient) approach would be to generate the 
   // numbers directly in the cylinder volume. But beware on the way to 
   // generate uniformly the numbers. Uniform in r,phi,z is wrong as it 
   // will be more dense in the center.


}