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pure function with an NIntegrate command

• To: mathgroup at smc.vnet.net
• Subject: [mg98957] pure function with an NIntegrate command
• From: Ruth Lazkoz Sáez <wtplasar at lg.ehu.es>
• Date: Wed, 22 Apr 2009 05:21:39 -0400 (EDT)
• References: <200904202312.TAA09654@smc.vnet.net> <23448530.1240284136702.JavaMail.root@n11> <200904210912.FAA24817@smc.vnet.net>

Hi,

I posted a question yesterday about pure functions. Probably when you 
receive this message someone would have
posted a solution. While I was waiting I managed to come closer to a 
possible solution, and the encountered another
problem.

This is my problem. I define a function

Efun[x_, y_, z_] := x + y + z

and then this other one, which does an integral using the previous function

fintnp[list_, y_, z_] :=NIntegrate[Efun[x, y, z], {x, 0, #}] & /@ list

In my computer I run

fintnp[{1, 2, 3, 4}, 0.2, 0.3] // Timing

and get {0.020001, {1., 3., 6., 10.}}

Now I want to construct a pure version of fintnp so that when the list 
is long I save a good load of time.

My first approach is

fint = Integrate[Efun[x, ##2], {x, 0, #1}] &

It gives the correct results but it is significantly slower because I 
use Integrate instead of NIntegrate, so I naively define

fintn= NIntegrate[Efun[x, ##2], {x, 0, #1}] &

and then get errors indicating the definition is not good. Can someone 
help me?

Thanks is advance.

Ruth

PD: Mathgroup is awesome, it has been amazingly useful for my work, and 
all the things I learn here made me a stronger Mathematica advocate anyday.

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