Fundamental Theorem of Calculus

The Fundamental Theorem of Calculus connects differentiation and integration, two core ideas in calculus. It states that if you have a function representing the accumulation of a quantity (like area under a curve), then its derivative (rate of change) is the original function. Conversely, if you differentiate an integral that sums up the values of a function, you get back the original function. Essentially, it shows that integration and differentiation are inverse processes, linking the area under a curve to the slope of the function at any point, providing a powerful way to analyze and compute many mathematical problems.