Electric Field of a Straight Wire (now with the attachment)

[The Head]

1. Homework Statement
The word document with the problem is attached below.


2. Homework Equations
dE=kdQ/r2²
Ex=Ecos∅

3. The Attempt at a Solution
dE=kdQ/r²
E=kλ∫dy/(x²+y²) (integrating from y= -L/2 to L/2)
Ex=2kλ∫xdy/(x²+y²)^3/2 (change integration to y= 0 to L/2, multiplying expression by 2)

Let y=xtan∅
dy=x(sec∅)² d∅

=2kxλ∫x(sec∅)²/x³(sec∅)³ d∅
=2kλ/x∫cos∅ d∅
=2kλ/x(sin∅)
=2kλ/x(sin(arctan(y/x)) (evaluated from y=0 to y=L/2)
=2kλ/x(y/(x²+y²)^1/2 (evaluated from 0->L/2)
=2kλ/x(L/2)(x²+(L²)/4)^1/2
=((1.8X10^10)λL/(2x))*(1/x²+(L²)/4)^1/2

This isn't the correct answer, though I don't know what actually is. I would appreciate any help or guidance!

 

[The Head]

Okay, I figured it out. I am using an online HW program and it just wanted the the answer in terms of epsilon, not a numerical value. Thanks anyway!