Question: How can I speed up this numerical integral?

Does anyone have any ideas on why this integral (third equation) is taking so long to solve/plot? Are there any hints on how to speed up the process?

I'm running Maple 2019.1, and it was chugging away for about 5 minutes before I pulled the plug.

If I have 2.14 & 10 or 2.14 & 20 as my plot arguments, it takes about 3 s. After 20, it just doesn't want to work.


J0:=(r,shk)-> BesselJ(0, 2*Pi*r*shk);

Jhk:=(s,shk,R)-> evalf((1/s)*Int(P1(r,R)*J0(r,shk)*sin(2*Pi*r*s), r=0..2*R));

plot(Jhk(s,2.14,38), s=0..5)
Please Wait...