An integral is a mathematical concept that represents the area under a curve on a graph. It is used to find the total value of a function over a specific interval.
A definite integral has specific limits of integration, meaning it calculates the area under the curve between two specific points. An indefinite integral does not have limits and represents the general antiderivative of a function.
An integral and differentiation are inverse operations of each other. Integration is the inverse of differentiation, meaning that the integral of a derivative of a function is equal to the original function.
Integrals are used in many fields of science and engineering, such as physics, chemistry, and economics. They are used to calculate areas, volumes, and even probabilities in real-world situations.
The fundamental theorem of calculus states that integration and differentiation are inverse operations, and they are linked by the fundamental theorem. This theorem allows us to evaluate integrals using antiderivatives.