Electric Field due to a charged line; With y as function of theta

Well the main problem here its once a i get the integral i do not how to put dy as function of thetha and then integrate ; at the end that’s what i get

Ex=integral (dE*cos[itex]\theta[/itex])=([itex]\lambda[/itex]/4[itex]\pi[/itex][itex]\epsilon[/itex])
times the integral of cos([itex]\theta[/itex])dy/x^2+y^2

where i can easily find the cosine and do the integral but i’m asked to express strictly "y" as function of thetha so as cos(θ)=x/√x^2+y^2 so 1/√x^2+y^2=cos^2(θ)/x^2

and i know that y=x*tan(θ) but i dont how to get "dy" graphically nor analytically;

Attached Images
File Type: jpg IMG_20140216_194726.jpg (29.2 KB)


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