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 given interval.
To compute an integral, you must first find the antiderivative of the function. This is done by using integration techniques, such as substitution, integration by parts, or partial fractions. Once the antiderivative is found, you can evaluate the integral by plugging in the upper and lower limits of the given interval.
A definite integral has specific limits of integration and gives a numerical value as a result. An indefinite integral does not have limits and gives an expression with a constant as a result.
The main types of integrals are definite and indefinite integrals. Other types include improper integrals, line integrals, surface integrals, and volume integrals. These types are used to solve different types of problems in various fields of mathematics and science.
Integration is used in many real-life applications, such as calculating areas and volumes in engineering, finding the center of mass in physics, and determining probabilities in statistics. It is also used in economics, biology, and other fields to model and solve problems involving continuous data.