I want to solve following double integration. I am stuck from long time. Any intermediate solution will also be appreciated.(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\int[/itex][itex]\int[/itex] dvb dvl (feven+fodd)

where,

feven = (r*(vl[itex]^{2}[/itex]+vb[itex]^{2}[/itex]))^(-2*[itex]\beta[/itex])*(potential - 0.5*(vl[itex]^{2}[/itex]+vb[itex]^{2}[/itex]+vr[itex]^{2}[/itex]))^(-3*[itex]\beta[/itex]+5.5), where [itex]\beta[/itex],potential and vr are some constant numbers

fodd = (1-[itex]\eta[/itex])*tanh(r*vl*cos(b)/1000)*feven

Where, [itex]\eta[/itex], r,b are constant numbers. Which means I want to marginalise (feven+fodd) over vl and vb.

Integration limits for vl and vb comes from energy equation. Limits are -[itex]\sqrt{2*potential - vb[itex]^{2}[/itex] - vr[itex]^{2}[/itex]}[/itex]<=vl<=[itex]\sqrt{2*potential - vb[itex]^{2}[/itex] - vr[itex]^{2}[/itex]}[/itex] and -[itex]\sqrt{2*potential - vr[itex]^{2}[/itex]}[/itex]<=vb<=[itex]\sqrt{2*potential - vr[itex]^{2}[/itex]}[/itex]

Also -3.5< =[itex]\beta[/itex] <1

and 0<= [itex]\eta[/itex] <=2

Any help will be highly appreciated

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# Solving the distribution function

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