Electric field from uniform charge of finite length

[Pyuruku]

Homework Statement

A uniform charge Q of length L is placed on the x-axis with one end at the origin as shown

a) Find the contribution dE (vector) to the electric field at P on the y-axis a distance y from the origin, from the charge at x in dx, in terms of Q, L, dx, ke, x and y

b) Find the total E (vector, in component form) from the whole line of charge at y on the y-axis in terms of Q, L, ke, y; also find E (vector) for |y| >> L

c) Use the result in (b) to obtain the behavior of E (vector, in component form) on the y-axis if L is infinite in the +x direction (left end remains at 0)

Homework Equations

I believe this is all I need?

The Attempt at a Solution

a)
$\huge dE = \frac{k\lambda dx}{r^2}<\frac{x}{r},\frac{y}{r}> = \frac{kQdx}{(x^2 + y^2)^{\frac{3}{2}}L}<x, y>$

This doesn't look right to me, and I'm a bit stuck on trying to integrate this... I'd assume you integrate with respect to X from 0 to L...

 

[Simon Bridge]

Well let's check it then: what was the reasoning you used to get to that equation?