Instead of simply computing the arithmetic mean over a sector, we can do ```math V_{\mathrm{avg}} = \frac{4}{\pi R^2} \int_{0}^{R} \int_{\theta_{\mathrm{start}}}^{\theta_{end}} V(r, \theta) r \mathrm{d}r \mathrm{d}\theta ``` and solve it with the trapezoidal method. It is convenient to first integrate over the azimuth and then over the radius. This way there will be fewer multiplications by $r$.