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## Homework Statement

Hi, i need to integrate a function which has a very nice structure. however, in case i cannot do the same, i would need a bound on the value of the integral. The problem is basically a minmization problem with n parameters. Please follow the link to acquaint your self with the problem.

http://img522.imageshack.us/img522/7894/equations640x480.gif [Broken]

## Homework Equations

http://img522.imageshack.us/img522/7894/equations640x480.gif [Broken]

here, d_i and theta_i are the distances and angles of point (x,y) from (xi,yi)

## The Attempt at a Solution

My attempt is as follows:

First of al, i could not directly integrate the function, so i tried to find a bound on it. I used the mod of the function (extension of triangle inequality) on the denominator to eliminate the sine squared in the denominator.

Upon doing that i tried to split the denominator through chebyshev sum inequality but didnt get anywhere.

I hope you can give me some insights into either solving the integral or getting a bound on its value.

thanks and regards

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