Hello I am interested in evaluating the following integral.
p[s_] := Sqrt[1 - (x - s)^2/(ct)^2]
initialWavePulse[x_] := Exp[-x^2/90]
Integrate[initialWavePulse[s]*{BesselJ[0, s]*(p[s]*t/(2 \[Tau])) +
1/p[s] *BesselJ[1, s] *(p[s]*t/(2 \[Tau])) } , {s, x - ct, x + ct}]
When I evaluate this integral, Mathematica just returns the input. Ultimately, I want the functional dependence of x and t as my answer.
Also, when I evaluate a simpler integral, it gives me a conditional expression which makes no sense:
Integrate[BesselJ[0, s], {s, x + ct, x - ct}]
Please help me go about solving this definite integral! Thank You!
Edit: To give you a little context, this is a part of the general solution to the linearly damped wave equation.
Integrate
, butNIntegrate
works. $\endgroup$