Why Integration Works | Fundamental Theorem of Calculus Explained

Integration, built from the problem it was invented to solve. Where the ∫ sign comes from, why "add one to the power and divide by the new power" actually works, and where the +C comes from. CHAPTERS 00:00 Introduction to what integration is 01:13 What ∫ f(x) dx actually means 02:26 A(x): the area so far, and how fast it grows 03:48 Proof: differentiate the area, get the curve back 05:45 Why "add one to the power, divide by the new power" works 06:24 Where the +C comes from 07:48 Definite integrals: F(b) − F(a), and why the C cancels 08:11 Worked example: area under y = 3x² + 4x from x = 1 to x = 2 09:03 Integration was never just about area Link to the differentiation video referenced:    • What Actually Happens When You Differentia...