• anonymous
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?
OCW Scholar - Multivariable Calculus
  • Stacey Warren - Expert
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  • jamiebookeater
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  • beginnersmind
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.

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