I'm gonna make him an offer he can't resist(ance)

The resistance of the conductor across its ends is given by: $R=\int_0^l{\cfrac{\rho dx}{\pi r^2}}$

where $x$ is the distance along the axis from the left end and $r$ is the radius of the cross section at $x$ , and $r = a + \cfrac{b-a}{l}x = 0.02+0.3x$

Therefore,

$\displaystyle R=\int_0^l{\cfrac{\rho dx}{\pi r^2}}=\cfrac{\rho}{\pi}\int_0^l{\cfrac{dx}{(0.02+0.3x)^2}}$

$\quad = \cfrac{\rho}{0.3\pi}\left[\cfrac{-1}{0.02+0.3x}\right]_0^l= \cfrac{6.28\times 10^{-8}}{0.3\times 3.1416}\left[\cfrac{1}{0.02}-\cfrac{1}{0.05}\right]$

$\quad = \cfrac{6.28\times 10^{-8}\times 30}{0.3\times 3.1416}=\boxed{2\times 10^{-6}\Omega}$

USE calculus