Mathematics
The Fundamental Theorem of Calculus: Linking Derivatives and Integrals
Quick fact
The Fundamental Theorem of Calculus is so powerful that it lets you compute a definite integral simply by evaluating an antiderivative at the endpoints—no need to sum up infinitely many slices. This single theorem turns a complex limit process into a two-minute calculation.
Why this is interesting
You've been told that differentiation finds slopes and integration finds areas—but what if they are actually two sides of the same coin? How can knowing a slope help you calculate an exact area?