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S[e^x]=f(u)^n

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## Homework Statement

I need to find the electric field along the Z-axis for a hemispherical open shell of radius R (open face down). the shell is oriented so its symmetrical about the Z axis.

## The Attempt at a Solution

What i've done is set it up, taken the vector from the origin (at the center of what would be the full sphere), and subtracted the vector bound to the z axis, to get the vector from the differential surface of the shell to an arbitrary point on the z axis. I then integrate, using spherical coordinates the 1/r^2 expression...

I can't seem to get this to work, can someone guide me through the right steps?, i've been trying to do this for about 7hrs now, and feel really stupid since i'm a 3rd year uni student majoring in physics....