NIntegrate vs. N[Integrate]

*To*: mathgroup at yoda.physics.unc.edu*Subject*: NIntegrate vs. N[Integrate]*From*: Mangalam Vasudaven <TVASUDAVE at cc.curtin.edu.au>*Date*: 21 Jul 1993 13:23:54 +0800

Hello Mathgroup, I was always under the impression that it is a lot more efficient to use NIntegrate when one is trying to get approximate values of definite integrals than surround it by N[]. But while playing around with some gamma integrals I found that NIntegrate took sixty times as much time as the second method. BTW, Mathematica Book, in page 683, confirms my original impression. p[x_]:= Integrate[(y^6)*(E^-y)/6!,{y,0,x}] NIntegrate[ p[x]*(1-p[x]),{x,0,200}] Now, the NIntegrate took 336.36 seconds. And N[Integrate[p[x]*(1-p[x]),{x,0,200},10] took just 5.66 seconds, giving an answer accurate to more decimal places than NIntegrate, incidently. Why does this happen? Being a novice to Mathematica, I could not figure out why. If it is of any relevance, I am running version 2.2 under windows. M. Vasudaven Curtin University of Technology Perth