A piece of conically-shaped material is placed in a circuit along the x-axis. The resistivity of this material varies as rho=(6*10^6)*x^4 (where x is measured in meters and rho is measured in ohm*meters), and its radius varies linearly as a function of x, ranging from r1=xinitial=3 cm to r2=xfinal=8.4 cm.
The Attempt at a Solution
Well current is flowing through the cone section so the cross sectional area is a circle, with the radius increasing proportional to x, in fact the are equal.
So dR=rho*dx/(2*pi*r) and dx=dr and x=r so plugging in for r
dR=(6*10^6)*r^4/(2*pi*r) dr = (3/pi * 10^6)*r^3 dr
which integrating from 0.03 to 0.084 m i got 11.69 Ohm, doesn't seem quite right did I mess up somewhere?