What is the power lost per foot?
You shouldn't need any derivatives or integration.

Remember the formula, \$\displaystyle R = \rho\frac{\ell}{A}\$? 

This formula is used for calculating the resistance of a conductor given resistivity (\$\displaystyle \rho\$), length of the conductor (\$\displaystyle \ell\$), and cross-sectional area (A). You need to use this formula to find resistance.

Once you've set up your equations (the one above, and the power equation you posted), you can solve for what the power loss is for \$\displaystyle \ell = 1 ft\$.

Personally I'd convert all those measurements to metric before anything else.