We derive the Fundamental Formula of the Algebraic Calculus, which allows us to define, and evaluate, the signed area of a polynomially parametrized curve, that is a de Casteljau Bezier curve. The approach is not via limits of Riemann sums, in fact infinite arguments do not appear. Rather we look at the crucial properties that linearly parametrized curves obey, and extending these to polynomially parametrized curves narrows down the possibilities and we get a unique formula.

Correction: at 20:11 slide 5: the '2c²A₂₀' should be '2c²A₁₁'. (Thanks to MeToo for catching that.)

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Here are the Wild Egg Maths Playlists (some available only to Members!)

Algebraic Calculus One (for the Open Learning Course) : [ Ссылка ]
Algebraic Calculus Two (for the Open Learning Course in preparation): [ Ссылка ]-

Advice for Mathematics Exploration (for Members only): [ Ссылка ]
Solving Polynomial Equations (Members only): [ Ссылка ]
Hexagrammum Mysticum (Members only): [ Ссылка ]_
Algebraic Calculus and de Casteljau Bezier curves (Members only): [ Ссылка ]
Exceptional Structures in Maths and Physics via Dynamics on Graphs (Members only): [ Ссылка ]
Maxel Inverses and Orthogonal Polynomials (for Members only): [ Ссылка ]

Triangle Centres: [ Ссылка ]
Six: An elementary course in pure mathematics: [ Ссылка ]

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Here are the Insights into Mathematics Playlists:

Maths and Music: [ Ссылка ]
Diffusion Symmetry: [ Ссылка ]
Elementary Mathematics (K-6) Explained: [ Ссылка ]?
list=PL8403C2F0C89B1333
Playing Go: [ Ссылка ]
Year 9 Maths: [ Ссылка ]
Ancient Mathematics: [ Ссылка ]
Wild West Banking: [ Ссылка ]
Sociology and Pure Mathematics: [ Ссылка ]
Old Babylonian Mathematics (with Daniel Mansfield): [ Ссылка ]?
list=PLIljB45xT85CdeBmQZ2QiCEnPQn5KQ6ov
Math History: [ Ссылка ]
Wild Trig: Intro to Rational Trigonometry: [ Ссылка ]
MathFoundations: [ Ссылка ]
Wild Linear Algebra: [ Ссылка ]
Famous Math Problems: [ Ссылка ]
Probability and Statistics: An Introduction: [ Ссылка ]
Boole's Logic and Circuit Analysis: [ Ссылка ]
Universal Hyperbolic Geometry: [ Ссылка ]
Differential Geometry: [ Ссылка ]
Algebraic Topology: [ Ссылка ]
Math Seminars: [ Ссылка ]

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