I have an equation for a term $z_i$:
$$ z_i = \ln\frac{a_iR+p_i}{T_o* tan\theta_i } $$
This represents a value in a grid, at location $i$, with the grid representing a geographic area. To get the average value of $z_i$ over the geographic area, I believe this is the proper representation:
$$ z_{avg} = \frac{1}{A}\int_A[\ln(\frac{a_iR+p_i}{T_o* tan\theta_i})]dA $$
In hoping to separate out parts of this equation for substitution into other equations, I develop this:
$$ z_{avg} = \frac{1}{A}\int_A[\ln(\frac{a_i}{T_o* tan\theta_i}) + \ln(R+\frac{p_i}{a_i})]dA $$
Is there anyway to pull the second ln() term out of the integral? Similarly, since this grid is made up of defined area cells, how quickly can I make the transition from using the indefinite integral to a mere summation from i to N for all grid cells? (with N being the total number of grid cells)
This is more a comment.
$\ln(\frac{a_iR+p_i}{T_o* tan\theta_i}) =\ln(a_iR+p_i)-\ln(T_o* tan\theta_i) $ so this would split the integral into two parts.