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:
\( \displaystyle \varepsilon(x) = \varepsilon_0 + kx, \text{ for } \left(0 < x \le \frac{d}{2}\right) \)
\( \varepsilon(x) = \varepsilon_0 + k(d-x), \text{ for }\left(\dfrac{d}{2} \le x \le d \right)\)
