)Integration is a mathematical concept that involves finding the area under a curve or the sum of infinitesimal parts to determine the total value of a function. It is used to solve problems related to area, volume, and accumulation.
The most commonly used methods of integration are the definite and indefinite integrals, substitution, integration by parts, and partial fractions. Other methods include trigonometric substitution, integration using tables, and numerical integration.
A definite integral has specific limits of integration, while an indefinite integral does not. In other words, a definite integral gives a single numerical value, while an indefinite integral gives a family of functions with the same derivative.
The choice of integration method depends on the complexity of the function and the techniques you are familiar with. It is often helpful to try different methods until one yields a solution. In some cases, it may also be necessary to use a combination of methods to solve a problem.
Integration has numerous applications in science, engineering, and economics. Some examples include calculating the trajectory of a projectile, finding the center of mass of an object, determining the volume of a complex shape, and analyzing the growth of a population over time.