A parallel plate capacitor with plate area ' \(A\) ' and distance of separation ' \(d\) ' is filled with a dielectric. W…

A parallel plate capacitor with plate area ' \(A\) ' and distance of separation ' \(d\) ' is filled with a dielectric. What is the capacity of the capacitor when permittivity of the dielectric varies as:
\[
\begin{aligned}
& \varepsilon(x)=\varepsilon_0+k x, \text { for }\left(0<x \leq \frac{d}{2}\right) \\
& \varepsilon(x)=\varepsilon_0+k(d-x), \text { for }\left(\frac{d}{2} \leq x \leq d\right)
\end{aligned}
\]