The explanation of a line integral in a vector field is very clear but I can't seem to find the lecture on a line integral in a scalar field. Is there one in the series?

Question

beginnersmind · Answer

The line integral is based on the dot product of two vectors, so there's no direct analogue for scalar fields.

You can take the one dimensional integral of a scalar field along a curve. I don't think this is very common but it's doable. If you have a curve parametrized by arc length rewrite your scalar field in terms of the parameter. This is now a single variable function that you can integrate the usual way.

For a two dimensional scalar field this can be used to calculate the area of a sheet below a certain path.