An integral is a mathematical concept used to calculate the area under a curve in a graph. It is also known as anti-derivative, as it is the reverse process of differentiation.
Integration is important because it allows us to find the area under a curve, which is useful in various real-world applications such as calculating volumes, work done, and center of mass.
The two main types of integrals are definite and indefinite integrals. A definite integral has specific limits of integration, while an indefinite integral does not have limits and represents a general solution.
There are various methods to solve an integral, including substitution, integration by parts, and trigonometric substitution. The most common approach is to use rules and formulas to simplify the integral and then solve it using algebraic techniques.
Integrals have numerous practical applications in various fields such as physics, engineering, economics, and statistics. They are used to calculate volumes of irregular objects, determine the work done by a force, and analyze growth and decay in business and population.
