Mathematics
The Fundamental Theorem of Calculus: Connecting Derivatives and Integrals
Quick fact
The Fundamental Theorem of Calculus is the reason that finding the area under a curve is as simple as evaluating an antiderivative at two points. It directly links the integral of a function to its antiderivative, turning a limit of sums into a straightforward calculation of differences.
Why this is interesting
You've probably noticed that finding the slope of a curve (differentiation) and finding the area under a curve (integration) seem like completely different tasks. But what if they were actually two sides of the same coin?