numerical integral solve for laser energy,S which is a function of z,t?

How to solve the spatiotemporal integral for the absorbed laser energy,S(all the other values J,L,tp are known)??

[Dyuman Joshi]

Solve what? I don't see an equation. Just an expression/function.

[John D'Errico]

I don't even see an integral. The answer is therefore 42.

Answer 1

[Walter Roberson]

syms J_abs L_op t_p t z
ln2 = log(sym(2));
Pi = sym(pi);

S(z,t) = 2/(sqrt(Pi/ln2)) * J_abs / (L_op * t_p) * exp(-z/L_op) * exp(-(4*ln2) * (t - 2*t_p).^2/t_p.^2)

S(z, t) = 

syms z_min z_max t_min t_max real
spatiotemporal_integral = int(int(S, t, t_min, t_max), z, z_min, z_max)

spatiotemporal_integral = 

simplify(spatiotemporal_integral, 'steps', 20)

ans = 

[Shahriar Shafin]

Thank u very much,Found my answer