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It's a uniform charge distribution question. Basically a half circle with radius [itex]r[/itex] and you have to find the electric field at a point that is along its x-axis. The [itex]E_y[/itex] component will be 0 because of symmetry. So all you need is is [itex]E_x[/itex]. The equation ends up being:

[tex]E_x=∫dEcosθ[/tex]

The only way I know how to solve this is using infinitesimals and finding one in terms of the other, like this:

[tex]dE=k\frac{dQ}{r^2}[/tex]

[tex]dQ=\frac{Q}{πr}dy[/tex]

[tex]dy=rdθ[/tex]

Then substituting those in all the way up so I have my integral in terms of θ.

So how would I go about solving this without using infinitesimals? Thanks