Theorems of Calculus

The Theorems of Calculus connect two main ideas: how things change and how to find the total amount accumulated. The first, the Fundamental Theorem of Calculus, says that if you know how a quantity changes, you can find the total accumulated over time by reversing the process—integrating. Conversely, differentiating a function that represents accumulated change recovers the original rate of change. These theorems unify differentiation (finding how things change) and integration (adding things up), allowing us to analyze complex systems like motion, growth, and areas efficiently and precisely.