Proof of Electromagnetic Identity: Puzzling Last Expression

[larginal]

Homework Statement

two identities in electromagentics

Relevant Equations

curl of gradientV = 0

I tried to understand proof of this identity from electromagnetics. but I was puzzled at the last expression.
why is that line integral of dV = 0 ?
In fact, I'm wondering if this expression makes sense.

 

[Orodruin]

If you had a curve integral along a curve $\Gamma$ with endpoints $p$ and $q$, what would the integral
$$
\int_\Gamma dV
$$
be? Note that
$$
\int_\Gamma dV = \int_0^1 \frac{dV}{dt} dt
$$
if we assume that $t$ is a curve parameter in the interval [0,1] parametrising the curve such that $p = \Gamma(0)$ and $q = \Gamma(1)$.

 

[larginal]

I got it. Thanks! is it your intention that you didn't complete the explanation to make me think?

 

[Orodruin]

is it your intention that you didn't complete the explanation to make me think?

Yes.