If I imagine the screen as the complex plane and the time axis coming out of the screen, e^(it) traces out a shape of a spring with its axis as the t axis.
My current intuition is we take an infinitesimally small section dt and multiply it with the value of the function at that point and sum it all up.
In the picture, if I were to integrate, I would take the sum of the areas of the little rectangles that two adjacent lines subtend in the interval I want to integrate. Is this way of thinking correct?
If not, then what would be the correct way of thinking?
If yes, then can the integral be visually calculated? And as in the question how can I visually calculate the integral in the interval [0,2*pi]?