Mr. Integral
Math notes/Calculus III/Vector Calculus

Scalar and Vector Line Integrals — Cheat sheet

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Core rule

ds=∥r′∥dt,ds=\|\mathbf r'\|dt, dr=r′dt.d\mathbf r=\mathbf r'dt.

Watch for

Scalar line integrals use speed. Work uses a dot product and an oriented path.