A conductor of uniform area of cross section A has a variable resistivity along its length. What will be the resistance of the conductor if `rho=rho_0(1+alphax^2)`, at length l.

Explanation

To find the resistance of a conductor with a variable resistivity given by \(\rho = \rho_0(1 + \alpha x^2)\) over its length \(L\), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We have a conductor of length \(L\) and uniform cross-sectional area \(A\). The resistivity \(\rho\) varies along its length according to the formula \(\rho = \rho_0(1 + \alpha x^2)\).

2. **Consider a Differential Element**: Take a small element of the conductor of length \(dx\) at a distance \(x\) from one end. The resistance \(dR\) of this small element can be expressed using the formula:
\[
...