Worked examples

Curves and line integrals

One sheet for each type of problem, with several worked examples of increasing difficulty: first the computation, then the explanation in words. Each sheet starts with links to the theory it uses.

• 1Regular curves and tangent vector
• 2Tangent lines to parametric curves
• 3Lengths of curves
• 4Line integrals of the first kind
• 5Centers of mass of homogeneous curves
• 6Work of a field along a curve
• 7Integrals over piecewise regular curves