# Math Help - System Modeling and integration problem. Need help?

1. ## Distance between the plates: Integration problem

There are two plates, green and blue as shown in the diagram below.

The green plate can move, due to which the distance R between the plates changes.

R at a height of h will be

R=(H d2+∆d1 h)/H

What will be the equation for integral of R for complete height H. Please explain the solution. I tried to solve it but came up with log(H)-log(0) in the equation. Log 0 cannot be solved.

$\frac1H\int_{0}^{H}\left(d_2+\frac{\Delta d_1}{H}\:h\right)dh=d_2+\frac{\Delta d_1}{2}$