Integration is a mathematical process that involves finding the area under a curve. It is the inverse operation of differentiation and is used in a variety of applications, including physics, engineering, and economics.
Integration is important because it allows us to find the exact value of a function at a particular point, as well as the total change in a function over a given interval. It also helps us solve real-world problems, such as finding the distance traveled by an object or the volume of a three-dimensional shape.
The main methods of integration are the substitution method, the integration by parts method, and the method of partial fractions. Other techniques include trigonometric substitution, improper integrals, and numerical integration.
To solve an integration problem, you need to first identify the function that you want to integrate. Then, choose an appropriate integration method and apply it to the function. Finally, evaluate the resulting expression to find the exact value or use numerical techniques to approximate it.
Integration is used in a variety of fields, including physics, engineering, economics, and biology. Some examples of real-world applications include calculating the work done by a force, finding the center of mass of an object, and determining the rate of change of a population over time.