I have the next doble integral:
$$ \int_{0}^{\infty}\int_{0}^{\infty}\frac{130000 E^{-0.36k^2}rSin[kr]Sin[kR]}{(72000+E^{2r})k^2R}drdk$$
In which the integration is made first in "r" and then is made in "k", finally giving a function of "R". The integral cannot be done analytically , so I used the next commands to find a table and the plot:
fc[k_?NumericQ, r_?NumericQ] = Simplify[130000*Exp[-0,36k^2]*r*Sin[kr]*Sin[kR]/((72000+Exp[2r])*k^2*R)] //
Expand]
and then:
tb=Table[{R,NIntegrate[ fc[k,r],{k,0,Infinity},{r,0,Infinity},Method -> {"LevinRule", "Points" -> 5}, PrecisionGoal -> 2, MaxRecursion -> 50]}, {R, 0.1, 20, 0.1}]
So finally I got the next plot:
I Have to find the x-coordinate for a given y-coordinate , namely, solving and equation, say, for a y=20 I should find aproximately x=10, however I don't know how to solve and equation involving a table or this kind of integral, I have to solve this later adding another horrific integral like the one here and do the same thing. Moreover, the integration is taking to much just with one integral !!. Can anybody help with these issues? Thanks in advance :D
kr
andkR
.... $\endgroup$ – Michael E2 Aug 29 '17 at 17:36