The Fundamental Theorem of Calculus

The Fundamental Theorem of Calculus connects two main ideas in calculus: differentiation and integration. It states that if you have a function and you calculate its integral (area under the curve) over an interval, you can find the original function's behavior (its slope) at any point within that interval. In essence, it shows that these processes are inverses of each other—integrating a function and then differentiating the result gives you back the original function. This powerful link helps us understand how things change and accumulate, foundational concepts in math and science.