I want to integrate the foll0wing expression to get a symbolic expression of the integration:

 1.0/( 4.0*
     Pi*((rr*rr) + (8.3*8.3) + (zz*zz) - (2.0*rr*8.3*Cos[ttt])))*
   ArcSin[zz/(((rr*rr) + (8.3*8.3) + (zz*zz) - (2.0*rr*8.3*
            Cos[ ttt]))^0.5)] - 20 Degree], {ttt, 0, 2*Pi}]

I want to get the expression in terms of rr and zz. Here rr, zz and ttt are threee variables. But I want to integrate for ttt varable for 0 to 2*Pi. Can anyone help me in this regard?


1 Answer 1


Mathematica cannot solve this integral, I think. But you can solve it numerically: First define

int[rr_, zz_] :=NIntegrate[1.0/(4.0*Pi*((rr*rr) + (8.3*8.3) + (zz*zz) - (2.0*rr*8.3*Cos[ttt])))*HeavisideTheta[ArcSin[zz/(((rr*rr) + (8.3*8.3) + (zz*zz) - (2.0*rr*8.3*Cos[ttt]))^0.5)] - 20 Degree], {ttt, 0, 2*Pi}]

to get parameter dependent integral.

Plot3D[int[r, z], {r, -3, 3}, {z, 0, 10}, AxesLabel -> {rr, zz}]

enter image description here


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