I was looking at the equation $e^{jwt}$ and visualizing it as a cylinder along the x-axis and yz is the complex plane. If we try to write this as a vector-valued function where:
$x$ = $t$, $z$ = $cos(wt)$, $y$ = $sin(wt)$
where $w$ = $2\pi f_{0}$. Then the picture will look like this:
source: Understanding DSP frequency domain
Now if I intrigate $\int e^{jwt}dt$ = $\int e^{jwx}dx$ what does it mean? Am I finding the area of the cylinder along $x$-axis?