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nickless
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?
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.