# [✓] Break a time consuming integration into pieces?

GROUPS:
 I am trying to calculate an expression which has the following form Sum[(-1)^(n+1) Bionomial[4,n] NIntegrate[S[n,x] Q[n,x] V[n,x] F[x], {x,0,2000} , WorkingPercision -> 5 ] , {n, 4} ] Where we have : G[x_ ] := 2 Pi x p[x] Exp[-2 Pi Integrate[t p[t], {t, 0, x}]] p[x_ ] := Piecewise[ {{0 , x > 140}} , Exp[ -0.0071* x] ]; S[n_ ,x_ ] := Exp[ -n x]; Q[n_ ,x_ ] := Product[ Exp[-2 Pi Integrate [1 - 1/(n x)^4 p[t] t , {t,x, Infinity }]] ,{n,4} ] V[n_ ,x_ ] := Product[ Exp[-2 Pi Integrate [1 - 1/(n x / t^2 )^4 (1-p[t]) t , {t, x^2 , Infinity }]] ,{n,4} ] F[x_ ] := G[x] Exp[Integrate[ -2 Pi (1- p[t]) t , {t, 0 , x }]] Unfortunately the evaluation takes so much time. Is there any way to break this expression into pieces and perform calculation separately ? p.s. I also tried limiting WorkingPercision and MaxRecursion but it didn't work.The acceptable WorkingPercision is 5 and the acceptable evaluation time is less than half an hour ! I appreciate your suggestions.
7 months ago
4 Replies
 Bill Simpson 2 Votes Are your five functions simple enough to paste (as code, not an image) into you original post?How long would an acceptable time be to complete this calculation?How little precision in the result would be acceptable to you?With those someone might be able to offer some ideas to help you.