Integrate vs NIntegrate

*To*: mathgroup at smc.vnet.net*Subject*: [mg46868] Integrate vs NIntegrate*From*: "Mukhtar Bekkali" <mbekkali at hotmail.com>*Date*: Fri, 12 Mar 2004 02:02:53 -0500 (EST)*Organization*: Iowa State University*Sender*: owner-wri-mathgroup at wolfram.com

I am confused why NIntegrate misbehaves on such a simple function as mine. Here is what I have: In: f=D[1/(1+(1+(a-b)^2)),a]; g=Integrate[f*b*(1-b)^2,{b,0,1},Assumptions->0<a<1]; FindRoot[g==0,{a,0,1}] Out: a->0.397207 However, since Integrate takes long, I tried to use NIntegrate instead and this is what I get In: f=D[1/(1+(1+(a-b)^2)),a]; g:=NIntegrate[f*b*(1-b)^2,{b,0,1}]; FindRoot[g==0,{a,0,1}] Out: a->1 or, FindRoot+NIntegrate give me the upper boundary of a. If I abandon the secant method and turn to Newton, i.e. use FindRoot[g==0,{a,0.5}] instead then I get the message that Jacobian is singular at a=0.5 and get no solution. Perturbing the starting value of a does not help. What is going on here? PS. Is there a way to get M5 to tackle the problem where: (1) I define some function f[x]:=NIntegrate[g[x,y],{y,0,1}], then (2) take the derivative of f[x] with respect to x, say h[x]:=f'[x] and then (3) Use FindRoot to find x such that h[x]==0

**Follow-Ups**:**Re: Integrate vs NIntegrate***From:*Anton Antonov <antonov@wolfram.com>