**Could you describe the differences/similarities between line integrals and regular integrals?**

We’ll assume a “regular” integral is a simple one-dimensional integral: \int_a^b f(x)\ dx. It involves only a scalar function f(x).

A line or path integral is \int_P\ \vec{F}(\vec{r})\cdot \vec{d \ell} where \vec{F} is a vector field and P is the path used to evaluate the integral.

A line or path integral is just a general form of a “regular” integral. Imagine two points in the xy-plane. In a “regular” integral, you draw a vertical line (the “bounding” lines) down from each point directly to the x-axis (the “reference” line). The “regular” integral is just the area in the xy-plane contained between these two vertical bounding lines. A line or path integral generalizes this concept but places no special emphasis on the x-axis as the “reference” line in particular. Instead, for a line or path integral, you can draw any line in the xy-plane and use that line as your reference line. Then you just draw a straight bounding line down from each point perpendicular to your reference line. The line or path integral is again just the area between the two bounding lines. A line or path integral is even more general than the description I just gave. For example, the reference line does not need to be a straight line between the two points. The reference line could be as curved and wavy as you like, but then it is more difficult to visualize the area being calculated.