MathGroup Archive 2006

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Solving integrals


Jens Benecke schrieb:
> Jens Benecke wrote:
> 
>> Hello everybody,
>>
>> I am trying to solve this integral:
>>
>> f :== int ( cos(x) / sqrt[A=C2=B2=C2=B7sin=C2=B2(x/2) + (Bx)=C2=B2 =
>> ] dx, x==0..N*2*pi
> 
> Hello,
> 
> sorry, this post apparently got mangled ("²" aka "^2" wasn't recognized).
> Here is the integral again:
> 
> f := int ( cos(x) / sqrt[ A*A*sin(x/2)*sin(x/2) + (Bx)^2] dx, x=0..N*2*pi
> 
> 
>> where N==(int)0..20, and A and B are small fixed values (around
>> 0.0001..0.05).
...

>> Thank you! :)
> 

Hi Jens,

  sorry, your integral does not converge on the interval [0, something], 
because your integrand is c_(-1)*x^(-1) + c_(1)*x + ... near x=0:

expr = Cos[x]/Sqrt[(a*Sin[x/2])^2 + (b*x)^2];
Normal[Simplify[Series[expr, {x, 0, 1}], a > 0 && b > 0]]//InputForm
Out[2]//InputForm=
  2/(Sqrt[a^2 + 4*b^2]*x) +
   ((-11*a^2 - 48*b^2)*x)/(12*(a^2 + 4*b^2)^(3/2))

Peter


  • Prev by Date: Re: simple question
  • Next by Date: Re: benchmark...why don't you send it back?
  • Previous by thread: Re: Solving integrals
  • Next by thread: Infinite integrals of Exp[-A x^2 + 2 B x]