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# How well can Mathematica do multivariate intergrating

Posted 11 years ago
 Dear Community,At the moment I'm using Maple, however i'm not satisfied by the way it does multivariate integration and I'm wondering if I should switch to Mathematica. Could someone tell me how Mathematica would deal with this simple example problem: A typical example (from gaussian beam optics) is to find the normalization constant N for$E(x_1)=N exp[-ik x^T Q x ]$using the conservation of energy1/N=$\int \int E(x_1) E(x_1)^* dx_1dy_1$where $*$ is complex conjugation,$Q \el R^{4x4}$ and has the property that $Q=Q^T$ and $x=[x_1 y_1 x_2 y_2 ]$.Thanks!Kind regards,Carlas
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Posted 11 years ago
 Multivariate integration by itself is no big deal.  Examples are scattered through    http://reference.wolfram.com/mathematica/ref/Integrate.html In[6]:= Integrate[ Sin*Sqrt, x, y]Out[6]=       2      3/2- ( - )  y         Cos    3In[7]:= Integrate[ Sin[x*Sqrt], x, y]Out[7]=      2 Sin[x Sqrt]-(   ----------------   )            x
Posted 11 years ago
 Could you translate the notation into something that does not assume as much background?
Posted 11 years ago
 Correction: $E(x_1)=N \int \int E_0(x_2) exp[-ik x^T Q x ]dx_2dy_2$