Calculating line or path integrals ↩

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created: 2021-10-19 23:48:10
modified: 2022-01-10 04:13:04

General steps

0. If the vector field is conservative, just use the gradient theorem
1. Parametrize the path with the lowest possible amount of variables (1 for a path, 2 for a surface, etc.) (it is a good practice to have the parametrization domain be )
2. If we integrate in a vector field, then calculate the normal or the tangential vector
3. Do a "coordinate transformation" into the domain of the parametrization in the integral
   • Derive the parametrization to get from
   • Plug in the parametrization into the functions in the integral
   • (Place in a normalized tangential/normal vector if needed)
4. Calculate the integral (use partial integration if needed)