Consider the nuclear reactor shown below:

Klown: dhat$()=ddr$

dvec$(r)=dxdydz$

Experimental results show that the steady$-$state neutron density in this reactor is given by:

$n(vec(r),E,$hat$())=$Cos$(x)e^{-E}{}^2$dvec$(r)dEdhat(),[\frac{\text{n}\text{e}\text{u}\text{t}\text{r}\text{o}\text{n}\text{s}}{c{m}^3*eV*\text{s}\text{t}\text{e}\text{r}\text{a}\text{d}\text{i}\text{a}\text{n}}]$

Based on this expression for angular neutron density, calculate the following:

The total number of neutrons in the reactor.

The total number of neutrons in the top half of the reactor $)>(5$ with energies between $0$ and $10eV$ that are moving to the right $)>(0$