Finding electric field 3 cm along a thin rod.

[jheld]

1. The problem statement, all variables and given/known data
The figure shows a thin rod of length L = 5.0 cm with total charge Q = 8.4 nC. What is the magnitude of the electric field E at x = 3.0 cm?

Figure in the attachment
2. Relevant equations
E = Kq/r^2
K = 8.99 * 10^9 N m^2/C^2;
r is the distance between the point and the charge.
Field for a line of charge:
E = KQ/(d*(d^2 + (L/2)^2)^(1/2))

3. The attempt at a solution
We have Q, L and "d". But I am still unable to get the answer.
When I plug in the values as they are (as what I think they are), I get 64458.88
Answer is: 2.7*10^5 N/C.

But, when I use linear charge density lambda = Q/L.
E = lambda/4*pi*epsilon_0 * distance, I get 2.2634 N/C. Do you think this is the right way to get it?
I am not sure why that equation does not work.
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution

[rl.bhat]

Field due to a small charge element at the point is given by
dE = k*dQ/r^2.
dQ = Q/L*dr
Hence E = Integration(dE) = k*Q/L*Int(dr/r^2).
Find the lower and upper limit of r,Substitute it in the integration to get the field.