# How well can Mathematica do multivariate intergrating

Posted 10 years ago
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 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 10 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 10 years ago
 Could you translate the notation into something that does not assume as much background?
Posted 10 years ago
 Correction: $E(x_1)=N \int \int E_0(x_2) exp[-ik x^T Q x ]dx_2dy_2$