Problem about electric potential and power transmitted down a cable

[Another]

When to use $V =-\int E ⋅ dl$ or $V =\int E ⋅ dl$ ?

When i use $V =-\int E ⋅ dl$. i can not show that P = IV because $\frac{ln \frac{b}{a}}{ln \frac{a}{b}} ≠ 1$

But the solution use $V =\int E ⋅ dl$ I'm concerned about using "minus" .

 

[vela]

The notation in the solutions is kind of sloppy, but it's easy enough to understand what was meant.

Assume that $\vec E$ points radially outward. Then the inner conductor is at a higher potential than the outer conductor so that $V = V_a - V_b$. So you have
$$V = V_a - V_b = -\int_b^a \vec E \cdot d\vec l = \int_a^b \vec E \cdot d \vec l.$$