The electric field inside an insulating infinite length solid cylinder

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    Electrostatics Gauss law
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TL;DR
Suppose there is a cylinder with infinity length and a radius R. At distance R/2, we have to find the electric field present inside. Confirmation needed regarding the method.
We are given volumetric charge density as ## \rho ## and we have to find the field at the distance R/2. Is my procedure valid?
 

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Looks good.
 

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