B Field in Semicircle Conductor

[Telcron]

Homework Statement

Basically there is conductor shell which is in the shape of a semicircle. It extends to infinity. (Think of this as like half of a cylindrical conductor shell). The radius of this shell is A, and it carries a total current of X. The shell extends infinitely into the page. What is B-Field (Magnetic Flux Density) at the center of this conductor? I attached image for clarity.

The Attempt at a Solution

I think that this problem should be easy to solve. Basically I find the B field due to a long wire of some current, and then change this to make it dB which I would integrate from 0 to pi to find the total B - Field as the superposition of all of the dB elements. Does this sound like the right approach? I know that the field due to a wire is (\mu* I)/(2*\pi*r) where r is the distance from the wire. For dB, this should be (\mu* dI)/(2*\pi*r). I am not quite sure how to set up this integral as I am not quite sure on how to express dI. Any suggestions?

Sorry for my bad English I do not speak it natively.

 

[Telcron]

Also I am sorry I am not good at the text formatting for the equation. The mu and the pi should not be superscript.

 

[Telcron]

So I think I have made progress. I have dB = (mudI) / (2piA) and I have dI as Idphi/pi. The B-Field from each dB is in the \phi directions, and as you integrate dB from 0 to \pi to get the whole B-Field the final field will point to the left because everything else will cancel out. The problem is when I take this integral I get 0. Any help? Please.