• To: mathgroup at smc.vnet.net
• Subject: [mg71379] Re: About NIntegrate
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Thu, 16 Nov 2006 00:53:15 -0500 (EST)
• Organization: The Open University, Milton Keynes, UK
• References: <ejf0mv\$3qv\$1@smc.vnet.net>

```Evanescence wrote:
> Dear all: My question is as follows:
>
> First I definite one variable is: a=Cosh[b]
> then,I definite two functions:
> one is :
> P[a_]=(((2)^(1/2))/Pi)*Integrate[(Cosh[I*t])/((a-Cosh[t])^^(1/2)),0,b,t]
Wrong syntax here------------------------------------------!!andhere!!!!
Must be

In[1]:=
a = Cosh[b];
P[a_] = (2^(1/2)/Pi)*Integrate[Cosh[I*t]/
(a - Cosh[t])^(1/2), {t, 0, b}]

Out[2]=
Cos[t]
Sqrt[2] Integrate[-----------------------, {t, 0, b}]
Sqrt[Cosh[b] - Cosh[t]]
-----------------------------------------------------
Pi

>   ! (I is the (-1)^(1/2)) ,the upper limit is b, the lower limit is 0)
> another
> is:G[a_]=((-(a-Cos[0.5])^(-3/2))/(3*(10)^2))*(Sin[0.5])^(2)+(1/1-0.5*0.1)*((0.025*(1+Cos[0.5])+0.4/999)*(1+Cos[0.5])^(1/2)*(ArcTan[(a-Cos[0.5])^(1/2)/(1+Cos[0.5])^(1/2)]-Pi/2)+(0.025*(1-Cos[0.5])-0.4/999)*(1+Cos[0.5])^(1/2)*(ArcTanh[(1-Cos[0.5])^(1/2)/(a-Cos[0.5])^(1/2)])
Missing parentheses. Should be

In[3]:=
G[a_] = (-(a - Cos[0.5])^(-3/2)/(3*10^2))*Sin[0.5]^2 +
(1/1 - 0.5*0.1)*(0.025*(1 + Cos[0.5]) + 0.4/999)*
(1 + Cos[0.5])^(1/2)*
(ArcTan[(a - Cos[0.5])^(1/2)/(1 + Cos[0.5])^
(1/2)] - Pi/2) + (0.025*(1 - Cos[0.5]) -
0.4/999)*(1 + Cos[0.5])^(1/2)*
ArcTanh[(1 - Cos[0.5])^(1/2)/(a - Cos[0.5])^(1/2)]

Out[3]=
Pi
0.0616242 (-(--) + ArcTan[0.729794 Sqrt[-0.877583 + Cosh[b]]]) +
2

0.349882
0.00364491 ArcTanh[-------------------------] -
Sqrt[-0.877583 + Cosh[b]]

0.000766163
------------------------
3/2
(-0.877583 + Cosh[b])

> then
> NIntegrate[P[a]*G[a],{a,1,Infinity}]
> but get error message is NIntegrate P[a]*G[a] is not numerical at
> {a}={2.}

The variable b does not seem to have any value. Did you mean something like

NIntegrate[P[b]*G[b], {b, 1, Infinity}]

Regards,
Jean-Marc

```

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