Fundamental Theorem of Calculus

Definition

The Fundamental Theorem of Calculus states that differentiation and integration are inverse operations. It connects these two fundamental concepts in calculus and allows us to evaluate definite integrals using antiderivatives.

Analogy

The Fundamental Theorem of Calculus can be compared to a magic trick where differentiation and integration are like two sides of the same coin. Just as you can turn a rabbit into a hat and then back into a rabbit, you can differentiate a function to find its rate of change and then integrate that rate of change to find the original function.

Related terms

Antiderivative: An antiderivative is the reverse process of differentiation. It finds a function whose derivative is equal to the given function.

Riemann sum: A Riemann sum is an approximation method for finding the area under a curve by dividing it into small rectangles.

Second Fundamental Theorem of Calculus: The Second Fundamental Theorem of Calculus establishes the connection between definite integrals and antiderivatives by providing a formula for evaluating definite integrals using antiderivatives.