Electric field from a circle arc

[nautola]

Homework Statement

Find the x-component of the electric field
at the origin due to the full arc length
for a charge of 3.8 μC and a radius of
1.9 m. The value of the Coulomb constant
is 8.98755 × 109 N · m2/C2.

Homework Equations

E = kq/r^2
dq = q dθ
λ = Q/ (R θ)

The Attempt at a Solution

I said E = kq/r^2
And so Ex = kq/r² * sinθ
and dEx = k*dq/r² * sinθ
and dq = λ ds
ds = R dθ
λ = q/s
so dq = Q/θ dθ

I get kq/r² ∫sinθ/ θ dθ

But when I input the answer from this integral (from the calculator) the answer is wrong.

 

[rl.bhat]

What is your answer?

 

[nautola]

I got 12968.1 N/C. Is my method correct?

 

[rl.bhat]

I don't think so.
dq = λ*ds, where
λ= q / s , ds = r*dθ and s = πr/2
Substituute these values in the expression of dE and find the integration taking limits θ = 0 to π/2