Uploaded February 2026 | Updated September 2026, 2 weeks ago
Here's a classic example of a line integral over the unit circle (i.e. a closed curve), but both Green's theorem and the fundamental theorem of line integrals fail! We will see what answers we get when we use those theorems, and compare that with the answer when we use parametrization. This classic example of a vector field is called "Vortex field".
Support this channel: patreon.com/c/blackpenredpen
0:00 Using Green's Theorem
3:38 Using the fundamental theorem of line integrals
7:12 Using parametrization (the actual answer)
8:50 The problem & why
#mathtutorials #lineintegrals #calculus3
Here's a classic example of a line integral over the unit circle (i.e. a closed curve), but both Green's theorem and the fundamental theorem of line integrals fail! We will see what answers we get when we use those theorems, and compare that with the answer when we use parametrization. This classic example of a vector field is called "Vortex field".
Support this channel: patreon.com/c/blackpenredpen
0:00 Using Green's Theorem
3:38 Using the fundamental theorem of line integrals
7:12 Using parametrization (the actual answer)
8:50 The problem & why
#mathtutorials #lineintegrals #calculus3
